cse 5331/7331 f'091 cse 5331/7331 fall 2009 data mining introductory and related topics...
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CSE 5331/7331 F'09 1
CSE 5331/7331CSE 5331/7331Fall 2009Fall 2009
DATA MININGDATA MININGIntroductory and Related TopicsIntroductory and Related Topics
Margaret H. DunhamMargaret H. DunhamDepartment of Computer Science and EngineeringDepartment of Computer Science and Engineering
Southern Methodist UniversitySouthern Methodist University
Slides extracted from Slides extracted from Data Mining, Introductory and Advanced TopicsData Mining, Introductory and Advanced Topics, Prentice Hall, 2002., Prentice Hall, 2002.
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Data Mining OutlineData Mining Outline
PART I PART I – IntroductionIntroduction– TechniquesTechniques
PART II – Core Topics PART III – Related Topics
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Introduction OutlineIntroduction Outline
Define data miningDefine data mining Data mining vs. databasesData mining vs. databases Basic data mining tasksBasic data mining tasks Data mining developmentData mining development Data mining issuesData mining issues
Goal:Goal: Provide an overview of data mining. Provide an overview of data mining.
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IntroductionIntroduction
Data is growing at a phenomenal rateData is growing at a phenomenal rate Users expect more sophisticated Users expect more sophisticated
informationinformation How?How?
UNCOVER HIDDEN INFORMATIONUNCOVER HIDDEN INFORMATION
DATA MININGDATA MINING
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Data Mining DefinitionData Mining Definition
Finding hidden information in a Finding hidden information in a databasedatabase
Fit data to a modelFit data to a model Similar termsSimilar terms
– Exploratory data analysisExploratory data analysis– Data driven discoveryData driven discovery– Deductive learningDeductive learning
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Data Mining AlgorithmData Mining Algorithm
Objective: Fit Data to a ModelObjective: Fit Data to a Model– DescriptiveDescriptive– PredictivePredictive
Preference – Technique to choose the Preference – Technique to choose the best modelbest model
Search – Technique to search the dataSearch – Technique to search the data– ““Query”Query”
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Database Processing vs. Data Database Processing vs. Data Mining ProcessingMining Processing
QueryQuery– Well definedWell defined– SQLSQL
QueryQuery– Poorly definedPoorly defined– No precise query languageNo precise query language
DataData– Operational dataOperational data
OutputOutput– PrecisePrecise– Subset of databaseSubset of database
DataData– Not operational dataNot operational data
OutputOutput– FuzzyFuzzy– Not a subset of databaseNot a subset of database
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Query ExamplesQuery Examples DatabaseDatabase
Data MiningData Mining
– Find all customers who have purchased milkFind all customers who have purchased milk
– Find all items which are frequently purchased Find all items which are frequently purchased with milk. (association rules)with milk. (association rules)
– Find all credit applicants with last name of Smith.Find all credit applicants with last name of Smith.– Identify customers who have purchased more Identify customers who have purchased more than $10,000 in the last month.than $10,000 in the last month.
– Find all credit applicants who are poor credit Find all credit applicants who are poor credit risks. (classification)risks. (classification)– Identify customers with similar buying habits. Identify customers with similar buying habits. (Clustering)(Clustering)
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Data Mining Models and TasksData Mining Models and Tasks
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Basic Data Mining TasksBasic Data Mining Tasks Classification Classification maps data into predefined groups maps data into predefined groups
or classesor classes– Supervised learningSupervised learning– Pattern recognitionPattern recognition– PredictionPrediction
RegressionRegression is used to map a data item to a real is used to map a data item to a real valued prediction variable.valued prediction variable.
Clustering Clustering groups similar data together into groups similar data together into clusters.clusters.– Unsupervised learningUnsupervised learning– SegmentationSegmentation– PartitioningPartitioning
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Basic Data Mining Tasks Basic Data Mining Tasks (cont’d)(cont’d)
Summarization Summarization maps data into subsets with maps data into subsets with associated simple descriptions.associated simple descriptions.– CharacterizationCharacterization– GeneralizationGeneralization
Link AnalysisLink Analysis uncovers relationships among uncovers relationships among data.data.– Affinity AnalysisAffinity Analysis– Association RulesAssociation Rules– Sequential Analysis determines sequential Sequential Analysis determines sequential
patterns.patterns.
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Ex: Time Series AnalysisEx: Time Series Analysis Example: Stock MarketExample: Stock Market Predict future valuesPredict future values Determine similar patterns over timeDetermine similar patterns over time Classify behaviorClassify behavior
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Data Mining vs. KDDData Mining vs. KDD
Knowledge Discovery in Databases Knowledge Discovery in Databases (KDD):(KDD): process of finding useful process of finding useful information and patterns in data.information and patterns in data.
Data Mining:Data Mining: Use of algorithms to Use of algorithms to extract the information and patterns extract the information and patterns derived by the KDD process. derived by the KDD process.
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KDD ProcessKDD Process
Selection:Selection: Obtain data from various sources. Obtain data from various sources. Preprocessing:Preprocessing: Cleanse data. Cleanse data. Transformation:Transformation: Convert to common format. Convert to common format.
Transform to new format.Transform to new format. Data Mining:Data Mining: Obtain desired results. Obtain desired results. Interpretation/Evaluation:Interpretation/Evaluation: Present results Present results
to user in meaningful manner.to user in meaningful manner.
Modified from [FPSS96C]
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KDD Process Ex: Web LogKDD Process Ex: Web Log Selection:Selection:
– Select log data (dates and locations) to useSelect log data (dates and locations) to use Preprocessing:Preprocessing:
– Remove identifying URLsRemove identifying URLs– Remove error logsRemove error logs
Transformation:Transformation: – Sessionize (sort and group)Sessionize (sort and group)
Data Mining:Data Mining: – Identify and count patternsIdentify and count patterns– Construct data structureConstruct data structure
Interpretation/Evaluation:Interpretation/Evaluation:– Identify and display frequently accessed sequences.Identify and display frequently accessed sequences.
Potential User Applications:Potential User Applications:– Cache predictionCache prediction– PersonalizationPersonalization
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Data Mining DevelopmentData Mining Development•Similarity Measures•Hierarchical Clustering•IR Systems•Imprecise Queries•Textual Data•Web Search Engines
•Bayes Theorem•Regression Analysis•EM Algorithm•K-Means Clustering•Time Series Analysis
•Neural Networks•Decision Tree Algorithms
•Algorithm Design Techniques•Algorithm Analysis•Data Structures
•Relational Data Model•SQL•Association Rule Algorithms•Data Warehousing•Scalability Techniques
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KDD IssuesKDD Issues
Human InteractionHuman Interaction OverfittingOverfitting OutliersOutliers InterpretationInterpretation Visualization Visualization Large DatasetsLarge Datasets High DimensionalityHigh Dimensionality
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KDD Issues (cont’d)KDD Issues (cont’d)
Multimedia DataMultimedia Data Missing DataMissing Data Irrelevant DataIrrelevant Data Noisy DataNoisy Data Changing DataChanging Data IntegrationIntegration ApplicationApplication
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Social Implications of DMSocial Implications of DM
Privacy Privacy ProfilingProfiling Unauthorized useUnauthorized use
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Data Mining MetricsData Mining Metrics
UsefulnessUsefulness Return on Investment (ROI)Return on Investment (ROI) AccuracyAccuracy Space/TimeSpace/Time
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Visualization TechniquesVisualization Techniques
GraphicalGraphical GeometricGeometric Icon-basedIcon-based Pixel-basedPixel-based HierarchicalHierarchical HybridHybrid
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Models Based on SummarizationModels Based on Summarization
Visualization:Visualization: Frequency distribution, mean, variance, Frequency distribution, mean, variance, median, mode, etc.median, mode, etc.
Box Plot:Box Plot:
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Scatter DiagramScatter Diagram
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Data Mining Techniques OutlineData Mining Techniques Outline
StatisticalStatistical– Point EstimationPoint Estimation– Models Based on SummarizationModels Based on Summarization– Bayes TheoremBayes Theorem– Hypothesis TestingHypothesis Testing– Regression and CorrelationRegression and Correlation
Similarity MeasuresSimilarity Measures Decision TreesDecision Trees Neural NetworksNeural Networks
– Activation FunctionsActivation Functions
Genetic AlgorithmsGenetic Algorithms
Goal:Goal: Provide an overview of basic data Provide an overview of basic data mining techniquesmining techniques
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Point EstimationPoint Estimation Point Estimate:Point Estimate: estimate a population estimate a population
parameter.parameter. May be made by calculating the parameter for a May be made by calculating the parameter for a
sample.sample. May be used to predict value for missing data.May be used to predict value for missing data. Ex: Ex:
– R contains 100 employeesR contains 100 employees– 99 have salary information99 have salary information– Mean salary of these is $50,000Mean salary of these is $50,000– Use $50,000 as value of remaining employee’s Use $50,000 as value of remaining employee’s
salary. salary. Is this a good idea?Is this a good idea?
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Estimation ErrorEstimation Error
Bias: Bias: Difference between expected value and Difference between expected value and actual value.actual value.
Mean Squared Error (MSE):Mean Squared Error (MSE): expected value expected value of the squared difference between the of the squared difference between the estimate and the actual value:estimate and the actual value:
Why square?Why square? Root Mean Square Error (RMSE)Root Mean Square Error (RMSE)
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Jackknife EstimateJackknife Estimate Jackknife Estimate:Jackknife Estimate: estimate of parameter is estimate of parameter is
obtained by omitting one value from the set of obtained by omitting one value from the set of observed values.observed values.
Ex: estimate of mean for X={xEx: estimate of mean for X={x1, … , x, … , xn}}
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Maximum Likelihood Maximum Likelihood Estimate (MLE)Estimate (MLE)
Obtain parameter estimates that maximize Obtain parameter estimates that maximize the probability that the sample data occurs for the probability that the sample data occurs for the specific model.the specific model.
Joint probability for observing the sample Joint probability for observing the sample data by multiplying the individual probabilities. data by multiplying the individual probabilities. Likelihood function: Likelihood function:
Maximize L.Maximize L.
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MLE ExampleMLE Example
Coin toss five times: {H,H,H,H,T}Coin toss five times: {H,H,H,H,T}
Assuming a perfect coin with H and T equally Assuming a perfect coin with H and T equally
likely, the likelihood of this sequence is: likely, the likelihood of this sequence is:
However if the probability of a H is 0.8 then:However if the probability of a H is 0.8 then:
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MLE Example (cont’d)MLE Example (cont’d) General likelihood formula:General likelihood formula:
Estimate for p is then 4/5 = 0.8Estimate for p is then 4/5 = 0.8
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Expectation-Maximization Expectation-Maximization (EM)(EM)
Solves estimation with incomplete data.Solves estimation with incomplete data. Obtain initial estimates for parameters.Obtain initial estimates for parameters. Iteratively use estimates for missing Iteratively use estimates for missing
data and continue until convergence.data and continue until convergence.
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EM ExampleEM Example
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EM AlgorithmEM Algorithm
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Bayes TheoremBayes Theorem
Posterior Probability:Posterior Probability: P(hP(h1|x|xi)) Prior Probability:Prior Probability: P(h P(h1)) Bayes Theorem:Bayes Theorem:
Assign probabilities of hypotheses given a data Assign probabilities of hypotheses given a data value.value.
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Bayes Theorem ExampleBayes Theorem Example Credit authorizations (hypotheses): Credit authorizations (hypotheses):
hh11=authorize purchase, h=authorize purchase, h2 = authorize after = authorize after further identification, hfurther identification, h3=do not authorize, =do not authorize, hh4= do not authorize but contact police= do not authorize but contact police
Assign twelve data values for all Assign twelve data values for all combinations of credit and income:combinations of credit and income:
From training data: P(hFrom training data: P(h11) = 60%; P(h) = 60%; P(h22)=20%; )=20%;
P(h P(h33)=10%; P(h)=10%; P(h44)=10%.)=10%.
1 2 3 4 Excellent x1 x2 x3 x4 Good x5 x6 x7 x8 Bad x9 x10 x11 x12
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Bayes Example(cont’d)Bayes Example(cont’d) Training Data:Training Data:
ID Income Credit Class xi 1 4 Excellent h1 x4 2 3 Good h1 x7 3 2 Excellent h1 x2 4 3 Good h1 x7 5 4 Good h1 x8 6 2 Excellent h1 x2 7 3 Bad h2 x11 8 2 Bad h2 x10 9 3 Bad h3 x11 10 1 Bad h4 x9
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Bayes Example(cont’d)Bayes Example(cont’d) Calculate P(xCalculate P(xii|h|hjj) and P(x) and P(xii))
Ex: P(xEx: P(x77|h|h11)=2/6; P(x)=2/6; P(x44|h|h11)=1/6; P(x)=1/6; P(x22|h|h11)=2/6; P(x)=2/6; P(x88||
hh11)=1/6; P(x)=1/6; P(xii|h|h11)=0 for all other x)=0 for all other xii.. Predict the class for xPredict the class for x44::
– Calculate P(hCalculate P(hjj|x|x44) for all h) for all hjj. . – Place xPlace x4 4 in class with largest value.in class with largest value.– Ex: Ex:
»P(hP(h11|x|x44)=(P(x)=(P(x44|h|h11)(P(h)(P(h11))/P(x))/P(x44)) =(1/6)(0.6)/0.1=1. =(1/6)(0.6)/0.1=1.
»xx4 4 in class hin class h11..
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Hypothesis TestingHypothesis Testing
Find model to explain behavior by Find model to explain behavior by creating and then testing a hypothesis creating and then testing a hypothesis about the data.about the data.
Exact opposite of usual DM approach.Exact opposite of usual DM approach. HH0 0 – Null hypothesis; Hypothesis to be – Null hypothesis; Hypothesis to be
tested.tested. HH1 1 – Alternative hypothesis– Alternative hypothesis
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Chi Squared StatisticChi Squared Statistic
O – observed valueO – observed value E – Expected value based on hypothesis.E – Expected value based on hypothesis.
Ex: Ex: – O={50,93,67,78,87}O={50,93,67,78,87}– E=75E=75– 22=15.55 and therefore significant=15.55 and therefore significant
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RegressionRegression
Predict future values based on past Predict future values based on past valuesvalues
Linear RegressionLinear Regression assumes linear assumes linear relationship exists.relationship exists.
y = cy = c00 + c + c11 x x11 + … + c + … + cnn x xnn
Find values to best fit the dataFind values to best fit the data
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Linear RegressionLinear Regression
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CorrelationCorrelation
Examine the degree to which the values Examine the degree to which the values for two variables behave similarly.for two variables behave similarly.
Correlation coefficient r:Correlation coefficient r:• 1 = perfect correlation1 = perfect correlation• -1 = perfect but opposite correlation-1 = perfect but opposite correlation• 0 = no correlation0 = no correlation
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Similarity MeasuresSimilarity Measures
Determine similarity between two objects.Determine similarity between two objects. Similarity characteristics:Similarity characteristics:
Alternatively, distance measure measure how Alternatively, distance measure measure how unlike or dissimilar objects are.unlike or dissimilar objects are.
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Similarity MeasuresSimilarity Measures
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Distance MeasuresDistance Measures
Measure dissimilarity between objectsMeasure dissimilarity between objects
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Twenty Questions GameTwenty Questions Game
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Decision TreesDecision Trees Decision Tree (DT):Decision Tree (DT):
– Tree where the root and each internal node is Tree where the root and each internal node is labeled with a question. labeled with a question.
– The arcs represent each possible answer to The arcs represent each possible answer to the associated question. the associated question.
– Each leaf node represents a prediction of a Each leaf node represents a prediction of a solution to the problem.solution to the problem.
Popular technique for classification; Leaf Popular technique for classification; Leaf node indicates class to which the node indicates class to which the corresponding tuple belongs.corresponding tuple belongs.
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Decision Tree ExampleDecision Tree Example
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Decision TreesDecision Trees
AA Decision Tree Model Decision Tree Model is a computational is a computational model consisting of three parts:model consisting of three parts:– Decision TreeDecision Tree– Algorithm to create the treeAlgorithm to create the tree– Algorithm that applies the tree to data Algorithm that applies the tree to data
Creation of the tree is the most difficult part.Creation of the tree is the most difficult part. Processing is basically a search similar to Processing is basically a search similar to
that in a binary search tree (although DT may that in a binary search tree (although DT may not be binary).not be binary).
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Decision Tree AlgorithmDecision Tree Algorithm
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DT DT Advantages/DisadvantagesAdvantages/Disadvantages
Advantages:Advantages:– Easy to understand. Easy to understand. – Easy to generate rulesEasy to generate rules
Disadvantages:Disadvantages:– May suffer from overfitting.May suffer from overfitting.– Classifies by rectangular partitioning.Classifies by rectangular partitioning.– Does not easily handle nonnumeric data.Does not easily handle nonnumeric data.– Can be quite large – pruning is necessary.Can be quite large – pruning is necessary.
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Neural Networks Neural Networks Based on observed functioning of human Based on observed functioning of human
brain. brain. (Artificial Neural Networks (ANN)(Artificial Neural Networks (ANN) Our view of neural networks is very simplistic. Our view of neural networks is very simplistic. We view a neural network (NN) from a We view a neural network (NN) from a
graphical viewpoint.graphical viewpoint. Alternatively, a NN may be viewed from the Alternatively, a NN may be viewed from the
perspective of matrices.perspective of matrices. Used in pattern recognition, speech Used in pattern recognition, speech
recognition, computer vision, and recognition, computer vision, and classification.classification.
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Neural NetworksNeural Networks Neural Network (NN)Neural Network (NN) is a directed graph is a directed graph
F=<V,A> with vertices V={1,2,…,n} and arcs F=<V,A> with vertices V={1,2,…,n} and arcs A={<i,j>|1<=i,j<=n}, with the following A={<i,j>|1<=i,j<=n}, with the following restrictions:restrictions:– V is partitioned into a set of input nodes, VV is partitioned into a set of input nodes, V II, ,
hidden nodes, Vhidden nodes, VHH, and output nodes, V, and output nodes, VOO..– The vertices are also partitioned into layers The vertices are also partitioned into layers – Any arc <i,j> must have node i in layer h-1 Any arc <i,j> must have node i in layer h-1
and node j in layer h.and node j in layer h.– Arc <i,j> is labeled with a numeric value wArc <i,j> is labeled with a numeric value w ijij..– Node i is labeled with a function fNode i is labeled with a function f ii..
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Neural Network ExampleNeural Network Example
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NN NodeNN Node
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NN Activation FunctionsNN Activation Functions
Functions associated with nodes in Functions associated with nodes in graph.graph.
Output may be in range [-1,1] or [0,1]Output may be in range [-1,1] or [0,1]
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NN Activation FunctionsNN Activation Functions
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NN LearningNN Learning
Propagate input values through graph.Propagate input values through graph. Compare output to desired output.Compare output to desired output. Adjust weights in graph accordingly.Adjust weights in graph accordingly.
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Neural NetworksNeural Networks
A A Neural Network ModelNeural Network Model is a computational is a computational model consisting of three parts:model consisting of three parts:– Neural Network graph Neural Network graph – Learning algorithm that indicates how Learning algorithm that indicates how
learning takes place.learning takes place.– Recall techniques that determine hew Recall techniques that determine hew
information is obtained from the network. information is obtained from the network. We will look at propagation as the recall We will look at propagation as the recall
technique.technique.
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NN AdvantagesNN Advantages
LearningLearning Can continue learning even after Can continue learning even after
training set has been applied.training set has been applied. Easy parallelizationEasy parallelization Solves many problemsSolves many problems
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NN DisadvantagesNN Disadvantages
Difficult to understandDifficult to understand May suffer from overfittingMay suffer from overfitting Structure of graph must be determined Structure of graph must be determined
a priori.a priori. Input values must be numeric.Input values must be numeric. Verification difficult.Verification difficult.
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Genetic AlgorithmsGenetic Algorithms Optimization search type algorithms. Optimization search type algorithms. Creates an initial feasible solution and Creates an initial feasible solution and
iteratively creates new “better” solutions.iteratively creates new “better” solutions. Based on human evolution and survival of the Based on human evolution and survival of the
fittest.fittest. Must represent a solution as an individual.Must represent a solution as an individual. Individual:Individual: string I=I string I=I11,I,I22,…,I,…,Inn where I where Ijj is in is in
given alphabet A. given alphabet A. Each character IEach character I j j is called a is called a genegene.. Population:Population: set of individuals. set of individuals.
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Genetic AlgorithmsGenetic Algorithms A A Genetic Algorithm (GA)Genetic Algorithm (GA) is a is a
computational model consisting of five parts:computational model consisting of five parts:– A starting set of individuals, P.A starting set of individuals, P.– CrossoverCrossover:: technique to combine two technique to combine two
parents to create offspring.parents to create offspring.– Mutation: Mutation: randomly change an individual.randomly change an individual.– Fitness: Fitness: determine the best individuals.determine the best individuals.– Algorithm which applies the crossover and Algorithm which applies the crossover and
mutation techniques to P iteratively using mutation techniques to P iteratively using the fitness function to determine the best the fitness function to determine the best individuals in P to keep. individuals in P to keep.
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Crossover ExamplesCrossover Examples
111 111
000 000
Parents Children
111 000
000 111
a) Single Crossover
111 111
Parents Children
111 000
000
a) Single Crossover
111 111
000 000
Parents
a) Multiple Crossover
111 111
000
Parents Children
111 000
000 111
Children
111 000
000 11100
11
00
11
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Genetic AlgorithmGenetic Algorithm
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GA Advantages/DisadvantagesGA Advantages/Disadvantages AdvantagesAdvantages
– Easily parallelizedEasily parallelized DisadvantagesDisadvantages
– Difficult to understand and explain to end Difficult to understand and explain to end users.users.
– Abstraction of the problem and method to Abstraction of the problem and method to represent individuals is quite difficult.represent individuals is quite difficult.
– Determining fitness function is difficult.Determining fitness function is difficult.– Determining how to perform crossover and Determining how to perform crossover and
mutation is difficult.mutation is difficult.
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Data Mining OutlineData Mining Outline
PART I - Introduction PART II – Core TopicsPART II – Core Topics
– ClassificationClassification– ClusteringClustering– Association RulesAssociation Rules
PART III – Related Topics
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Classification OutlineClassification Outline
Classification Problem OverviewClassification Problem Overview Classification TechniquesClassification Techniques
– RegressionRegression– DistanceDistance– Decision TreesDecision Trees– RulesRules– Neural NetworksNeural Networks
Goal:Goal: Provide an overview of the classification Provide an overview of the classification problem and introduce some of the basic problem and introduce some of the basic algorithmsalgorithms
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Classification ProblemClassification Problem Given a database D={tGiven a database D={t11,t,t22,…,t,…,tnn} and a set } and a set
of classes C={Cof classes C={C11,…,C,…,Cmm}, the }, the Classification ProblemClassification Problem is to define a is to define a mapping f:Dmapping f:DC where each tC where each tii is assigned is assigned to one class.to one class.
Actually divides D into Actually divides D into equivalence equivalence classesclasses..
PredictionPrediction isis similar, but may be viewed similar, but may be viewed as having infinite number of classes.as having infinite number of classes.
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Classification ExamplesClassification Examples
Teachers classify students’ grades as Teachers classify students’ grades as A, B, C, D, or F. A, B, C, D, or F.
Identify mushrooms as poisonous or Identify mushrooms as poisonous or edible.edible.
Predict when a river will flood.Predict when a river will flood. Identify individuals with credit risks. Identify individuals with credit risks. Speech recognitionSpeech recognition Pattern recognitionPattern recognition
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Classification Ex: GradingClassification Ex: Grading
If x >= 90 then grade If x >= 90 then grade =A.=A.
If 80<=x<90 then If 80<=x<90 then grade =B.grade =B.
If 70<=x<80 then If 70<=x<80 then grade =C.grade =C.
If 60<=x<70 then If 60<=x<70 then grade =D.grade =D.
If x<50 then grade =F.If x<50 then grade =F.
>=90<90
x
>=80<80
x
>=70<70
x
F
B
A
>=60<50
x C
D
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Classification Ex: Letter Classification Ex: Letter RecognitionRecognition
View letters as constructed from 5 components:
Letter C
Letter E
Letter A
Letter D
Letter F
Letter B
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Classification TechniquesClassification Techniques
Approach:Approach:1.1. Create specific model by evaluating Create specific model by evaluating
training data (or using domain training data (or using domain experts’ knowledge).experts’ knowledge).
2.2. Apply model developed to new data.Apply model developed to new data. Classes must be predefinedClasses must be predefined Most common techniques use DTs, Most common techniques use DTs,
NNs, or are based on distances or NNs, or are based on distances or statistical methods.statistical methods.
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Defining ClassesDefining Classes
Partitioning Based
Distance Based
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Issues in ClassificationIssues in Classification
Missing DataMissing Data– IgnoreIgnore– Replace with assumed valueReplace with assumed value
Measuring PerformanceMeasuring Performance– Classification accuracy on test dataClassification accuracy on test data– Confusion matrixConfusion matrix– OC CurveOC Curve
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Height Example DataHeight Example DataName Gender Height Output1 Output2 Kristina F 1.6m Short Medium Jim M 2m Tall Medium Maggie F 1.9m Medium Tall Martha F 1.88m Medium Tall Stephanie F 1.7m Short Medium Bob M 1.85m Medium Medium Kathy F 1.6m Short Medium Dave M 1.7m Short Medium Worth M 2.2m Tall Tall Steven M 2.1m Tall Tall Debbie F 1.8m Medium Medium Todd M 1.95m Medium Medium Kim F 1.9m Medium Tall Amy F 1.8m Medium Medium Wynette F 1.75m Medium Medium
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Classification PerformanceClassification Performance
True Positive
True NegativeFalse Positive
False Negative
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Confusion Matrix ExampleConfusion Matrix Example
Using height data example with Output1 Using height data example with Output1 correct and Output2 actual assignmentcorrect and Output2 actual assignment
Actual Assignment Membership Short Medium Tall Short 0 4 0 Medium 0 5 3 Tall 0 1 2
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Operating Characteristic CurveOperating Characteristic Curve
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RegressionTopicsRegressionTopics
Linear RegressionLinear Regression Nonlinear RegressionNonlinear Regression Logistic RegressionLogistic Regression MetricsMetrics
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Remember High School?Remember High School?
Y= mx + bY= mx + b You need two points to determine a You need two points to determine a
straight line.straight line. You need two points to find values for m You need two points to find values for m
and b.and b.
THIS IS REGRESSIONTHIS IS REGRESSION
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RegressionRegression Assume data fits a predefined functionAssume data fits a predefined function Determine best values for Determine best values for regression regression
coefficientscoefficients cc00,c,c11,…,c,…,cnn.. Assume an error: y = cAssume an error: y = c00+c+c11xx11+…+c+…+cnnxxnn+ Estimate error using mean squared error for
training set:
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Linear RegressionLinear Regression Assume data fits a predefined functionAssume data fits a predefined function Determine best values for Determine best values for regression regression
coefficientscoefficients cc00,c,c11,…,c,…,cnn.. Assume an error: y = cAssume an error: y = c00+c+c11xx11+…+c+…+cnnxxnn+ Estimate error using mean squared error for
training set:
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Classification Using Linear Classification Using Linear RegressionRegression
Division:Division: Use regression function to Use regression function to divide area into regions. divide area into regions.
PredictionPrediction: Use regression function to : Use regression function to predict a class membership function. predict a class membership function. Input includes desired class.Input includes desired class.
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DivisionDivision
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PredictionPrediction
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Linear Regression Poor FitLinear Regression Poor Fit
Why use sum of least squares?http://curvefit.com/sum_of_squares.htmLinear doesn’t always work well
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Nonlinear RegressionNonlinear Regression
Data does not nicely fit a straight lineData does not nicely fit a straight line Fit data to a curveFit data to a curve Many possible functionsMany possible functions Not as easy and straightforward as Not as easy and straightforward as
linear regressionlinear regression How nonlinear regression works:How nonlinear regression works:
http://curvefit.com/how_nonlin_works.htm
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Logistic RegressionLogistic Regression
Generalized linear modelGeneralized linear model Predict discrete outcomePredict discrete outcome
– Binomial (binary) logistic regressionBinomial (binary) logistic regression– Multinomial logistic regressionMultinomial logistic regression
One dependent variableOne dependent variable Logistic Regression by Gerard E. DallalLogistic Regression by Gerard E. Dallal
http://www.jerrydallal.com/LHSP/logistic.htm
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Logistic Regression (cont’d)Logistic Regression (cont’d)
Log Odds Function: Log Odds Function:
P is probability that outcome is 1P is probability that outcome is 1 Odds – The probability the event occurs Odds – The probability the event occurs
divided by the probability that it does not divided by the probability that it does not occuroccur
Log Odds function is strictly increasing as p Log Odds function is strictly increasing as p increasesincreases
xp
p10)
1log(
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Why Log Odds?Why Log Odds?
Shape of curve is desirableShape of curve is desirable Relationship to probabilityRelationship to probability Range – to +Range – to +
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P-valueP-value
The probability that a variable has a The probability that a variable has a value greater than the observed valuevalue greater than the observed value
http://en.wikipedia.org/wiki/P-value http://sportsci.org/resource/stats/pvalues.html
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CovarianceCovariance
Degree to which two variables vary in the Degree to which two variables vary in the same mannersame manner
Correlation is normalized and covariance Correlation is normalized and covariance is notis not
http://www.ds.unifi.it/VL/VL_EN/expect/expect3.html
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ResidualResidual
ErrorError Difference between desired output and Difference between desired output and
predicted outputpredicted output May actually use sum of squaresMay actually use sum of squares
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Classification Using DistanceClassification Using Distance Place items in class to which they are Place items in class to which they are
“closest”.“closest”. Must determine distance between an item Must determine distance between an item
and a class.and a class. Classes represented byClasses represented by
– Centroid:Centroid: Central value. Central value.– Medoid:Medoid: Representative point. Representative point.– Individual pointsIndividual points
Algorithm: KNNAlgorithm: KNN
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K Nearest Neighbor (KNN):K Nearest Neighbor (KNN):
Training set includes classes.Training set includes classes. Examine K items near item to be Examine K items near item to be
classified.classified. New item placed in class with the most New item placed in class with the most
number of close items.number of close items. O(q) for each tuple to be classified. O(q) for each tuple to be classified.
(Here q is the size of the training set.)(Here q is the size of the training set.)
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KNNKNN
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KNN AlgorithmKNN Algorithm
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Classification Using Decision Classification Using Decision TreesTrees
Partitioning based:Partitioning based: Divide search Divide search space into rectangular regions.space into rectangular regions.
Tuple placed into class based on the Tuple placed into class based on the region within which it falls.region within which it falls.
DT approaches differ in how the tree is DT approaches differ in how the tree is built: built: DT InductionDT Induction
Internal nodes associated with attribute Internal nodes associated with attribute and arcs with values for that attribute.and arcs with values for that attribute.
Algorithms: ID3, C4.5, CARTAlgorithms: ID3, C4.5, CART
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Decision TreeDecision TreeGiven: Given:
– D = {tD = {t11, …, t, …, tnn} where t} where tii=<t=<ti1i1, …, t, …, tihih> > – Database schema contains {ADatabase schema contains {A11, A, A22, …, A, …, Ahh}}– Classes C={CClasses C={C11, …., C, …., Cmm}}
Decision or Classification TreeDecision or Classification Tree is is a tree associated a tree associated with D such thatwith D such that– Each internal node is labeled with attribute, AEach internal node is labeled with attribute, A ii
– Each arc is labeled with predicate which can be Each arc is labeled with predicate which can be applied to attribute at parentapplied to attribute at parent
– Each leaf node is labeled with a class, CEach leaf node is labeled with a class, C jj
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DT InductionDT Induction
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DT Splits Area DT Splits Area
Gender
Height
M
F
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Comparing DTsComparing DTs
BalancedDeep
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DT IssuesDT Issues
Choosing Splitting AttributesChoosing Splitting Attributes Ordering of Splitting AttributesOrdering of Splitting Attributes SplitsSplits Tree StructureTree Structure Stopping CriteriaStopping Criteria Training DataTraining Data PruningPruning
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Decision Tree Induction is often based on Decision Tree Induction is often based on Information TheoryInformation Theory
SoSo
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InformationInformation
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DT Induction DT Induction
When all the marbles in the bowl are When all the marbles in the bowl are mixed up, little information is given. mixed up, little information is given.
When the marbles in the bowl are all When the marbles in the bowl are all from one class and those in the other from one class and those in the other two classes are on either side, more two classes are on either side, more information is given.information is given.
Use this approach with DT Induction !Use this approach with DT Induction !
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Information/EntropyInformation/Entropy Given probabilitites pGiven probabilitites p11, p, p22, .., p, .., pss whose sum is whose sum is
1, 1, EntropyEntropy is defined as:is defined as:
Entropy measures the amount of randomness Entropy measures the amount of randomness or surprise or uncertainty.or surprise or uncertainty.
Goal in classificationGoal in classification– no surpriseno surprise– entropy = 0entropy = 0
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EntropyEntropy
log (1/p) H(p,1-p)
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ID3ID3 Creates tree using information theory Creates tree using information theory
concepts and tries to reduce expected concepts and tries to reduce expected number of comparison..number of comparison..
ID3 chooses split attribute with the highest ID3 chooses split attribute with the highest information gain:information gain:
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ID3 Example (Output1)ID3 Example (Output1) Starting state entropy:Starting state entropy:4/15 log(15/4) + 8/15 log(15/8) + 3/15 log(15/3) = 0.43844/15 log(15/4) + 8/15 log(15/8) + 3/15 log(15/3) = 0.4384 Gain using gender:Gain using gender:
– Female: 3/9 log(9/3)+6/9 log(9/6)=0.2764Female: 3/9 log(9/3)+6/9 log(9/6)=0.2764– Male: 1/6 (log 6/1) + 2/6 log(6/2) + 3/6 log(6/3) = Male: 1/6 (log 6/1) + 2/6 log(6/2) + 3/6 log(6/3) =
0.43920.4392– Weighted sum: (9/15)(0.2764) + (6/15)(0.4392) = Weighted sum: (9/15)(0.2764) + (6/15)(0.4392) =
0.341520.34152– Gain: 0.4384 – 0.34152 = 0.09688Gain: 0.4384 – 0.34152 = 0.09688
Gain using height:Gain using height:0.4384 – (2/15)(0.301) = 0.39830.4384 – (2/15)(0.301) = 0.3983
Choose height as first splitting attributeChoose height as first splitting attribute
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C4.5C4.5 ID3 ID3 favors attributes with large number of favors attributes with large number of
divisionsdivisions Improved version of ID3:Improved version of ID3:
– Missing DataMissing Data– Continuous DataContinuous Data– PruningPruning– RulesRules– GainRatio:GainRatio:
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CARTCART
Create Binary TreeCreate Binary Tree Uses entropyUses entropy Formula to choose split point, s, for node t:Formula to choose split point, s, for node t:
PPLL,P,PRR probability that a tuple in the training set probability that a tuple in the training set
will be on the left or right side of the tree.will be on the left or right side of the tree.
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CART ExampleCART Example At the start, there are six choices for At the start, there are six choices for
split point split point (right branch on equality):(right branch on equality):– P(Gender)=P(Gender)=2(6/15)(9/15)(2/15 + 4/15 + 3/15)=0.2242(6/15)(9/15)(2/15 + 4/15 + 3/15)=0.224
– P(1.6) = 0P(1.6) = 0– P(1.7) = P(1.7) = 2(2/15)(13/15)(0 + 8/15 + 3/15) = 0.1692(2/15)(13/15)(0 + 8/15 + 3/15) = 0.169
– P(1.8) = P(1.8) = 2(5/15)(10/15)(4/15 + 6/15 + 3/15) = 0.3852(5/15)(10/15)(4/15 + 6/15 + 3/15) = 0.385
– P(1.9) = P(1.9) = 2(9/15)(6/15)(4/15 + 2/15 + 3/15) = 0.2562(9/15)(6/15)(4/15 + 2/15 + 3/15) = 0.256
– P(2.0) = P(2.0) = 2(12/15)(3/15)(4/15 + 8/15 + 3/15) = 0.322(12/15)(3/15)(4/15 + 8/15 + 3/15) = 0.32
Split at 1.8Split at 1.8
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Classification Using Neural Classification Using Neural NetworksNetworks
Typical NN structure for classification:Typical NN structure for classification:– One output node per classOne output node per class– Output value is class membership function valueOutput value is class membership function value
Supervised learning Supervised learning For each tuple in training set, propagate it For each tuple in training set, propagate it
through NN. Adjust weights on edges to through NN. Adjust weights on edges to improve future classification. improve future classification.
Algorithms: Propagation, Backpropagation, Algorithms: Propagation, Backpropagation, Gradient DescentGradient Descent
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NN Issues NN Issues
Number of source nodesNumber of source nodes Number of hidden layersNumber of hidden layers Training dataTraining data Number of sinksNumber of sinks InterconnectionsInterconnections WeightsWeights Activation FunctionsActivation Functions Learning TechniqueLearning Technique When to stop learningWhen to stop learning
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Decision Tree vs. Neural Decision Tree vs. Neural NetworkNetwork
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PropagationPropagation
Tuple Input
Output
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NN Propagation AlgorithmNN Propagation Algorithm
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Example PropagationExample Propagation
© Prentie Hall
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NN LearningNN Learning
Adjust weights to perform better with the Adjust weights to perform better with the associated test data.associated test data.
Supervised:Supervised: Use feedback from Use feedback from knowledge of correct classification.knowledge of correct classification.
Unsupervised:Unsupervised: No knowledge of No knowledge of correct classification needed.correct classification needed.
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NN Supervised LearningNN Supervised Learning
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Supervised LearningSupervised Learning
Possible error values assuming output from Possible error values assuming output from node i is ynode i is yii but should be d but should be d ii::
Change weights on arcs based on estimated Change weights on arcs based on estimated errorerror
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NN BackpropagationNN Backpropagation
Propagate changes to weights Propagate changes to weights backward from output layer to input backward from output layer to input layer.layer.
Delta Rule:Delta Rule: w wijij= c x= c xijij (d (dj j – y– yjj)) Gradient Descent:Gradient Descent: technique to modify technique to modify
the weights in the graph.the weights in the graph.
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BackpropagationBackpropagation
Error
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Backpropagation AlgorithmBackpropagation Algorithm
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Gradient DescentGradient Descent
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Gradient Descent AlgorithmGradient Descent Algorithm
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Output Layer LearningOutput Layer Learning
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Hidden Layer LearningHidden Layer Learning
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Types of NNsTypes of NNs
Different NN structures used for Different NN structures used for different problems.different problems.
PerceptronPerceptron Self Organizing Feature MapSelf Organizing Feature Map Radial Basis Function NetworkRadial Basis Function Network
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PerceptronPerceptron
Perceptron is one of the simplest NNs.Perceptron is one of the simplest NNs. No hidden layers.No hidden layers.
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Perceptron ExamplePerceptron Example
Suppose:Suppose:– Summation: S=3xSummation: S=3x11+2x+2x22-6-6
– Activation: if S>0 then 1 else 0Activation: if S>0 then 1 else 0
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Self Organizing Feature Map Self Organizing Feature Map (SOFM)(SOFM)
Competitive Unsupervised LearningCompetitive Unsupervised Learning Observe how neurons work in brain:Observe how neurons work in brain:
– Firing impacts firing of those nearFiring impacts firing of those near– Neurons far apart inhibit each otherNeurons far apart inhibit each other– Neurons have specific nonoverlapping Neurons have specific nonoverlapping
taskstasks Ex: Kohonen NetworkEx: Kohonen Network
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Kohonen NetworkKohonen Network
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Kohonen NetworkKohonen Network
Competitive Layer – viewed as 2D gridCompetitive Layer – viewed as 2D grid Similarity between competitive nodes and Similarity between competitive nodes and
input nodes:input nodes:– Input: X = <xInput: X = <x11, …, x, …, xhh>>
– Weights: <wWeights: <w1i1i, … , w, … , whihi>>
– Similarity defined based on dot productSimilarity defined based on dot product
Competitive node most similar to input “wins”Competitive node most similar to input “wins” Winning node weights (as well as Winning node weights (as well as
surrounding node weights) increased.surrounding node weights) increased.
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Radial Basis Function NetworkRadial Basis Function Network
RBF function has Gaussian shapeRBF function has Gaussian shape RBF NetworksRBF Networks
– Three LayersThree Layers– Hidden layer – Gaussian activation Hidden layer – Gaussian activation
functionfunction– Output layer – Linear activation functionOutput layer – Linear activation function
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Radial Basis Function NetworkRadial Basis Function Network
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Classification Using RulesClassification Using Rules Perform classification using If-Then Perform classification using If-Then
rulesrules Classification Rule:Classification Rule: r = <a,c> r = <a,c>
Antecedent, ConsequentAntecedent, Consequent May generate from from other May generate from from other
techniques (DT, NN) or generate techniques (DT, NN) or generate directly.directly.
Algorithms: Gen, RX, 1R, PRISMAlgorithms: Gen, RX, 1R, PRISM
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Generating Rules from DTsGenerating Rules from DTs
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Generating Rules ExampleGenerating Rules Example
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Generating Rules from NNsGenerating Rules from NNs
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1R Algorithm1R Algorithm
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1R Example1R Example
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PRISM AlgorithmPRISM Algorithm
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PRISM ExamplePRISM Example
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Decision Tree vs. Rules Decision Tree vs. Rules
Tree has implied Tree has implied order in which order in which splitting is splitting is performed.performed.
Tree created based Tree created based on looking at all on looking at all classes.classes.
Rules have no Rules have no ordering of ordering of predicates.predicates.
Only need to look at Only need to look at one class to one class to generate its rules.generate its rules.
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Clustering OutlineClustering Outline
Clustering Problem OverviewClustering Problem Overview Clustering TechniquesClustering Techniques
– Hierarchical AlgorithmsHierarchical Algorithms– Partitional AlgorithmsPartitional Algorithms– Genetic AlgorithmGenetic Algorithm– Clustering Large DatabasesClustering Large Databases
Goal:Goal: Provide an overview of the clustering Provide an overview of the clustering problem and introduce some of the basic problem and introduce some of the basic algorithmsalgorithms
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Clustering ExamplesClustering Examples
SegmentSegment customer database based on customer database based on similar buying patterns.similar buying patterns.
Group houses in a town into Group houses in a town into neighborhoods based on similar neighborhoods based on similar features.features.
Identify new plant speciesIdentify new plant species Identify similar Web usage patternsIdentify similar Web usage patterns
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Clustering ExampleClustering Example
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Clustering HousesClustering Houses
Size BasedGeographic Distance Based
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Clustering vs. ClassificationClustering vs. Classification
No prior knowledgeNo prior knowledge– Number of clustersNumber of clusters– Meaning of clustersMeaning of clusters
Unsupervised learningUnsupervised learning
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Clustering IssuesClustering Issues
Outlier handlingOutlier handling Dynamic dataDynamic data Interpreting resultsInterpreting results Evaluating resultsEvaluating results Number of clustersNumber of clusters Data to be usedData to be used ScalabilityScalability
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Impact of Outliers on Impact of Outliers on ClusteringClustering
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Clustering ProblemClustering Problem
Given a database D={tGiven a database D={t11,t,t22,…,t,…,tnn} of tuples } of tuples and an integer value k, the and an integer value k, the Clustering Clustering ProblemProblem is to define a mapping is to define a mapping f:Df:D{1,..,k} where each t{1,..,k} where each tii is assigned to is assigned to one cluster Kone cluster Kjj, 1<=j<=k., 1<=j<=k.
A A ClusterCluster, K, Kjj, contains precisely those , contains precisely those tuples mapped to it.tuples mapped to it.
Unlike classification problem, clusters Unlike classification problem, clusters are not known a priori.are not known a priori.
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Types of Clustering Types of Clustering
HierarchicalHierarchical – Nested set of clusters – Nested set of clusters created.created.
Partitional Partitional – One set of clusters – One set of clusters created.created.
Incremental Incremental – Each element handled – Each element handled one at a time.one at a time.
SimultaneousSimultaneous – All elements handled – All elements handled together.together.
Overlapping/Non-overlappingOverlapping/Non-overlapping
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Clustering ApproachesClustering Approaches
Clustering
Hierarchical Partitional Categorical Large DB
Agglomerative Divisive Sampling Compression
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Cluster ParametersCluster Parameters
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Distance Between ClustersDistance Between Clusters Single LinkSingle Link: smallest distance between points: smallest distance between points Complete Link:Complete Link: largest distance between points largest distance between points Average Link:Average Link: average distance between pointsaverage distance between points Centroid:Centroid: distance between centroidsdistance between centroids
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Hierarchical ClusteringHierarchical Clustering
Clusters are created in levels actually Clusters are created in levels actually creating sets of clusters at each level.creating sets of clusters at each level.
AgglomerativeAgglomerative– Initially each item in its own clusterInitially each item in its own cluster– Iteratively clusters are merged togetherIteratively clusters are merged together– Bottom UpBottom Up
DivisiveDivisive– Initially all items in one clusterInitially all items in one cluster– Large clusters are successively dividedLarge clusters are successively divided– Top DownTop Down
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Hierarchical AlgorithmsHierarchical Algorithms
Single LinkSingle Link MST Single LinkMST Single Link Complete LinkComplete Link Average LinkAverage Link
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DendrogramDendrogram
Dendrogram:Dendrogram: a tree data a tree data structure which illustrates structure which illustrates hierarchical clustering hierarchical clustering techniques.techniques.
Each level shows clusters Each level shows clusters for that level.for that level.– Leaf – individual clustersLeaf – individual clusters– Root – one clusterRoot – one cluster
A cluster at level i is the A cluster at level i is the union of its children clusters union of its children clusters at level i+1.at level i+1.
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Levels of ClusteringLevels of Clustering
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Agglomerative ExampleAgglomerative ExampleAA BB CC DD EE
AA 00 11 22 22 33
BB 11 00 22 44 33
CC 22 22 00 11 55
DD 22 44 11 00 33
EE 33 33 55 33 00
BA
E C
D
4
Threshold of
2 3 51
A B C D E
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MST ExampleMST Example
AA BB CC DD EE
AA 00 11 22 22 33
BB 11 00 22 44 33
CC 22 22 00 11 55
DD 22 44 11 00 33
EE 33 33 55 33 00
BA
E C
D
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Agglomerative AlgorithmAgglomerative Algorithm
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Single LinkSingle Link View all items with links (distances) View all items with links (distances)
between them.between them. Finds maximal connected components Finds maximal connected components
in this graph.in this graph. Two clusters are merged if there is at Two clusters are merged if there is at
least one edge which connects them.least one edge which connects them. Uses threshold distances at each level.Uses threshold distances at each level. Could be agglomerative or divisive.Could be agglomerative or divisive.
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MST Single Link AlgorithmMST Single Link Algorithm
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Single Link ClusteringSingle Link Clustering
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Partitional ClusteringPartitional Clustering
NonhierarchicalNonhierarchical Creates clusters in one step as Creates clusters in one step as
opposed to several steps.opposed to several steps. Since only one set of clusters is output, Since only one set of clusters is output,
the user normally has to input the the user normally has to input the desired number of clusters, k.desired number of clusters, k.
Usually deals with static sets.Usually deals with static sets.
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Partitional AlgorithmsPartitional Algorithms
MSTMST Squared ErrorSquared Error K-MeansK-Means Nearest NeighborNearest Neighbor PAMPAM BEABEA GAGA
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MST AlgorithmMST Algorithm
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Squared ErrorSquared Error
Minimized squared errorMinimized squared error
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Squared Error AlgorithmSquared Error Algorithm
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K-MeansK-Means Initial set of clusters randomly chosen.Initial set of clusters randomly chosen. Iteratively, items are moved among sets Iteratively, items are moved among sets
of clusters until the desired set is of clusters until the desired set is reached.reached.
High degree of similarity among High degree of similarity among elements in a cluster is obtained.elements in a cluster is obtained.
Given a cluster KGiven a cluster Kii={t={ti1i1,t,ti2i2,…,t,…,timim}, the }, the
cluster meancluster mean is m is mii = (1/m)(t = (1/m)(ti1i1 + … + t + … + timim))
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K-Means ExampleK-Means Example Given: {2,4,10,12,3,20,30,11,25}, k=2Given: {2,4,10,12,3,20,30,11,25}, k=2 Randomly assign means: mRandomly assign means: m11=3,m=3,m22=4=4 KK11={2,3}, K={2,3}, K22={4,10,12,20,30,11,25}, ={4,10,12,20,30,11,25},
mm11=2.5,m=2.5,m22=16=16 KK11={2,3,4},K={2,3,4},K22={10,12,20,30,11,25}, m={10,12,20,30,11,25}, m11=3,m=3,m22=18=18 KK11={2,3,4,10},K={2,3,4,10},K22={12,20,30,11,25}, ={12,20,30,11,25},
mm11=4.75,m=4.75,m22=19.6=19.6 KK11={2,3,4,10,11,12},K={2,3,4,10,11,12},K22={20,30,25}, m={20,30,25}, m11=7,m=7,m22=25=25 Stop as the clusters with these means are the Stop as the clusters with these means are the
same.same.
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K-Means AlgorithmK-Means Algorithm
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Nearest NeighborNearest Neighbor
Items are iteratively merged into the Items are iteratively merged into the existing clusters that are closest.existing clusters that are closest.
IncrementalIncremental Threshold, t, used to determine if items Threshold, t, used to determine if items
are added to existing clusters or a new are added to existing clusters or a new cluster is created.cluster is created.
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Nearest Neighbor AlgorithmNearest Neighbor Algorithm
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PAMPAM
Partitioning Around Medoids (PAM) Partitioning Around Medoids (PAM) (K-Medoids)(K-Medoids)
Handles outliers well.Handles outliers well. Ordering of input does not impact results.Ordering of input does not impact results. Does not scale well.Does not scale well. Each cluster represented by one item, Each cluster represented by one item,
called the called the medoid.medoid. Initial set of k medoids randomly chosen.Initial set of k medoids randomly chosen.
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PAMPAM
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PAM Cost CalculationPAM Cost Calculation At each step in algorithm, medoids are At each step in algorithm, medoids are
changed if the overall cost is improved.changed if the overall cost is improved. CCjihjih – cost change for an item t – cost change for an item t jj associated associated
with swapping medoid twith swapping medoid t ii with non-medoid t with non-medoid thh..
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PAM AlgorithmPAM Algorithm
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BEABEA Bond Energy AlgorithmBond Energy Algorithm Database design (physical and logical)Database design (physical and logical) Vertical fragmentationVertical fragmentation Determine affinity (bond) between attributes Determine affinity (bond) between attributes
based on common usage.based on common usage. Algorithm outline:Algorithm outline:
1.1. Create affinity matrixCreate affinity matrix
2.2. Convert to BOND matrix Convert to BOND matrix
3.3. Create regions of close bondingCreate regions of close bonding
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BEABEA
Modified from [OV99]
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Genetic Algorithm ExampleGenetic Algorithm Example
{{A,B,C,D,E,F,G,H}A,B,C,D,E,F,G,H} Randomly choose initial solution:Randomly choose initial solution:
{A,C,E} {B,F} {D,G,H} or{A,C,E} {B,F} {D,G,H} or10101000, 01000100, 0001001110101000, 01000100, 00010011
Suppose crossover at point four and Suppose crossover at point four and choose 1choose 1stst and 3 and 3rdrd individuals: individuals:10100011, 01000100, 0001100010100011, 01000100, 00011000
What should termination criteria be?What should termination criteria be?
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GA AlgorithmGA Algorithm
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Clustering Large DatabasesClustering Large Databases
Most clustering algorithms assume a large Most clustering algorithms assume a large data structure which is memory resident.data structure which is memory resident.
Clustering may be performed first on a Clustering may be performed first on a sample of the database then applied to the sample of the database then applied to the entire database.entire database.
AlgorithmsAlgorithms– BIRCHBIRCH– DBSCANDBSCAN– CURECURE
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Desired Features for Large Desired Features for Large DatabasesDatabases
One scan (or less) of DBOne scan (or less) of DB OnlineOnline Suspendable, stoppable, resumableSuspendable, stoppable, resumable IncrementalIncremental Work with limited main memoryWork with limited main memory Different techniques to scan (e.g. Different techniques to scan (e.g.
sampling)sampling) Process each tuple onceProcess each tuple once
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BIRCHBIRCH Balanced Iterative Reducing and Balanced Iterative Reducing and
Clustering using HierarchiesClustering using Hierarchies Incremental, hierarchical, one scanIncremental, hierarchical, one scan Save clustering information in a tree Save clustering information in a tree Each entry in the tree contains Each entry in the tree contains
information about one clusterinformation about one cluster New nodes inserted in closest entry in New nodes inserted in closest entry in
treetree
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Clustering FeatureClustering Feature CT Triple: (N,LS,SS)CT Triple: (N,LS,SS)
– N: Number of points in clusterN: Number of points in cluster– LS: Sum of points in the clusterLS: Sum of points in the cluster– SS: Sum of squares of points in the clusterSS: Sum of squares of points in the cluster
CF TreeCF Tree– Balanced search treeBalanced search tree– Node has CF triple for each childNode has CF triple for each child– Leaf node represents cluster and has CF value Leaf node represents cluster and has CF value
for each subcluster in it.for each subcluster in it.– Subcluster has maximum diameterSubcluster has maximum diameter
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BIRCH AlgorithmBIRCH Algorithm
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Improve ClustersImprove Clusters
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DBSCANDBSCAN
Density Based Spatial Clustering of Density Based Spatial Clustering of Applications with NoiseApplications with Noise
Outliers will not effect creation of cluster.Outliers will not effect creation of cluster. InputInput
– MinPts MinPts – minimum number of points in – minimum number of points in clustercluster
– EpsEps – for each point in cluster there must – for each point in cluster there must be another point in it less than this distance be another point in it less than this distance away.away.
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DBSCAN Density ConceptsDBSCAN Density Concepts
Eps-neighborhood:Eps-neighborhood: Points within Eps Points within Eps distance of a point.distance of a point.
Core point:Core point: Eps-neighborhood dense enough Eps-neighborhood dense enough (MinPts)(MinPts)
Directly density-reachable:Directly density-reachable: A point p is A point p is directly density-reachable from a point q if the directly density-reachable from a point q if the distance is small (Eps) and q is a core point.distance is small (Eps) and q is a core point.
Density-reachable:Density-reachable: A point si density- A point si density-reachable form another point if there is a path reachable form another point if there is a path from one to the other consisting of only core from one to the other consisting of only core points.points.
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Density ConceptsDensity Concepts
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DBSCAN AlgorithmDBSCAN Algorithm
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CURECURE
Clustering Using RepresentativesClustering Using Representatives Use many points to represent a cluster Use many points to represent a cluster
instead of only oneinstead of only one Points will be well scatteredPoints will be well scattered
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CURE ApproachCURE Approach
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CURE AlgorithmCURE Algorithm
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CURE for Large DatabasesCURE for Large Databases
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Comparison of Clustering Comparison of Clustering TechniquesTechniques
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Association Rules OutlineAssociation Rules OutlineGoal: Provide an overview of basic Association Provide an overview of basic Association
Rule mining techniquesRule mining techniques Association Rules Problem OverviewAssociation Rules Problem Overview
– Large itemsetsLarge itemsets Association Rules AlgorithmsAssociation Rules Algorithms
– AprioriApriori– SamplingSampling– PartitioningPartitioning– Parallel AlgorithmsParallel Algorithms
Comparing TechniquesComparing Techniques Incremental AlgorithmsIncremental Algorithms Advanced AR TechniquesAdvanced AR Techniques
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Example: Market Basket DataExample: Market Basket Data Items frequently purchased together:Items frequently purchased together:
Bread Bread PeanutButterPeanutButter Uses:Uses:
– Placement Placement – AdvertisingAdvertising– SalesSales– CouponsCoupons
Objective: increase sales and reduce Objective: increase sales and reduce costscosts
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Association Rule DefinitionsAssociation Rule Definitions
Set of items:Set of items: I={I I={I11,I,I22,…,I,…,Imm}}
Transactions:Transactions: D={t D={t11,t,t22, …, t, …, tnn}, t}, tjj I I
Itemset:Itemset: {I {Ii1i1,I,Ii2i2, …, I, …, Iikik} } I I Support of an itemset:Support of an itemset: Percentage of Percentage of
transactions which contain that itemset.transactions which contain that itemset. Large (Frequent) itemset:Large (Frequent) itemset: Itemset Itemset
whose number of occurrences is above whose number of occurrences is above a threshold.a threshold.
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Association Rules ExampleAssociation Rules Example
I = { Beer, Bread, Jelly, Milk, PeanutButter}
Support of {Bread,PeanutButter} is 60%
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Association Rule DefinitionsAssociation Rule Definitions
Association Rule (AR): Association Rule (AR): implication X implication X Y where X,Y Y where X,Y I and X I and X Y = Y = ;;
Support of AR (s) X Support of AR (s) X YY: : Percentage of transactions that Percentage of transactions that contain X contain X YY
Confidence of AR (Confidence of AR () X ) X Y: Y: Ratio of Ratio of number of transactions that contain X number of transactions that contain X Y to the number that contain X Y to the number that contain X
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Association Rules Ex (cont’d)Association Rules Ex (cont’d)
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Association Rule ProblemAssociation Rule Problem Given a set of items I={IGiven a set of items I={I11,I,I22,…,I,…,Imm} and a } and a
database of transactions D={tdatabase of transactions D={t11,t,t22, …, t, …, tnn} } where twhere tii={I={Ii1i1,I,Ii2i2, …, I, …, Iikik} and I} and Iijij I, the I, the Association Rule ProblemAssociation Rule Problem is to is to identify all association rulesidentify all association rules X X Y Y with with a minimum support and confidence.a minimum support and confidence.
Link AnalysisLink Analysis NOTE:NOTE: Support of Support of X X Y Y is same as is same as
support of X support of X Y. Y.
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Association Rule TechniquesAssociation Rule Techniques
1.1. Find Large Itemsets.Find Large Itemsets.
2.2. Generate rules from frequent itemsets.Generate rules from frequent itemsets.
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Algorithm to Generate ARsAlgorithm to Generate ARs
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AprioriApriori
Large Itemset Property:Large Itemset Property:
Any subset of a large itemset is large.Any subset of a large itemset is large. Contrapositive:Contrapositive:
If an itemset is not large, If an itemset is not large,
none of its supersets are large.none of its supersets are large.
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Large Itemset PropertyLarge Itemset Property
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Apriori Ex (cont’d)Apriori Ex (cont’d)
s=30% = 50%
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Apriori AlgorithmApriori Algorithm
1.1. CC11 = Itemsets of size one in I; = Itemsets of size one in I;
2.2. Determine all large itemsets of size 1, LDetermine all large itemsets of size 1, L1;1;
3. i = 1;
4.4. RepeatRepeat
5.5. i = i + 1;i = i + 1;
6.6. CCi i = Apriori-Gen(L= Apriori-Gen(Li-1i-1););
7.7. Count CCount Cii to determine L to determine L i;i;
8.8. until no more large itemsets found;until no more large itemsets found;
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Apriori-GenApriori-Gen
Generate candidates of size i+1 from Generate candidates of size i+1 from large itemsets of size i.large itemsets of size i.
Approach used: join large itemsets of Approach used: join large itemsets of size i if they agree on i-1 size i if they agree on i-1
May also prune candidates who have May also prune candidates who have subsets that are not large.subsets that are not large.
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Apriori-Gen ExampleApriori-Gen Example
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Apriori-Gen Example (cont’d)Apriori-Gen Example (cont’d)
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Apriori Adv/DisadvApriori Adv/Disadv
Advantages:Advantages:– Uses large itemset property.Uses large itemset property.– Easily parallelizedEasily parallelized– Easy to implement.Easy to implement.
Disadvantages:Disadvantages:– Assumes transaction database is memory Assumes transaction database is memory
resident.resident.– Requires up to m database scans.Requires up to m database scans.
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SamplingSampling Large databasesLarge databases Sample the database and apply Apriori to the Sample the database and apply Apriori to the
sample. sample. Potentially Large Itemsets (PL):Potentially Large Itemsets (PL): Large Large
itemsets from sampleitemsets from sample Negative Border (BD Negative Border (BD -- ): ):
– Generalization of Apriori-Gen applied to Generalization of Apriori-Gen applied to itemsets of varying sizes.itemsets of varying sizes.
– Minimal set of itemsets which are not in PL, Minimal set of itemsets which are not in PL, butbut whose subsets are all in PL. whose subsets are all in PL.
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Negative Border ExampleNegative Border Example
PL PL BD-(PL)
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Sampling AlgorithmSampling Algorithm
1.1. DDss = sample of Database D; = sample of Database D;
2.2. PL = Large itemsets in DPL = Large itemsets in Dss using smalls; using smalls;
3.3. C = PL C = PL BDBD--(PL);(PL);4.4. Count C in Database using s;Count C in Database using s;
5.5. ML = large itemsets in BDML = large itemsets in BD--(PL);(PL);6.6. If ML = If ML = then donethen done
7.7. else C = repeated application of BDelse C = repeated application of BD-;-;
8.8. Count C in Database;Count C in Database;
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Sampling ExampleSampling Example Find AR assuming s = 20%Find AR assuming s = 20% DDss = { t = { t11,t,t22}} Smalls = 10%Smalls = 10% PL = {{Bread}, {Jelly}, {PeanutButter}, PL = {{Bread}, {Jelly}, {PeanutButter},
{Bread,Jelly}, {Bread,PeanutButter}, {Jelly, {Bread,Jelly}, {Bread,PeanutButter}, {Jelly, PeanutButter}, {Bread,Jelly,PeanutButter}}PeanutButter}, {Bread,Jelly,PeanutButter}}
BDBD--(PL)={{Beer},{Milk}}(PL)={{Beer},{Milk}} ML = {{Beer}, {Milk}} ML = {{Beer}, {Milk}} Repeated application of BDRepeated application of BD- - generates all generates all
remaining itemsetsremaining itemsets
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Sampling Adv/DisadvSampling Adv/Disadv
Advantages:Advantages:– Reduces number of database scans to one Reduces number of database scans to one
in the best case and two in worst.in the best case and two in worst.– Scales better.Scales better.
Disadvantages:Disadvantages:– Potentially large number of candidates in Potentially large number of candidates in
second passsecond pass
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PartitioningPartitioning
Divide database into partitions DDivide database into partitions D11,D,D22,,…,D…,Dpp
Apply Apriori to each partitionApply Apriori to each partition Any large itemset must be large in at Any large itemset must be large in at
least one partition.least one partition.
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Partitioning AlgorithmPartitioning Algorithm
1.1. Divide D into partitions DDivide D into partitions D11,D,D22,…,D,…,Dp;p;
2. For I = 1 to p do
3.3. LLii = Apriori(D = Apriori(Dii););
4.4. C = LC = L11 … … L Lpp;;
5.5. Count C on D to generate L;Count C on D to generate L;
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Partitioning ExamplePartitioning Example
D1
D2
S=10%
L1 ={{Bread}, {Jelly}, {Bread}, {Jelly}, {PeanutButter}, {PeanutButter}, {Bread,Jelly}, {Bread,Jelly}, {Bread,PeanutButter}, {Bread,PeanutButter}, {Jelly, PeanutButter}, {Jelly, PeanutButter}, {Bread,Jelly,PeanutButter}}{Bread,Jelly,PeanutButter}}
L2 ={{Bread}, {Milk}, {Bread}, {Milk}, {PeanutButter}, {Bread,Milk}, {PeanutButter}, {Bread,Milk}, {Bread,PeanutButter}, {Milk, {Bread,PeanutButter}, {Milk, PeanutButter}, PeanutButter}, {Bread,Milk,PeanutButter}, {Bread,Milk,PeanutButter}, {Beer}, {Beer,Bread}, {Beer}, {Beer,Bread}, {Beer,Milk}}{Beer,Milk}}
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Partitioning Adv/DisadvPartitioning Adv/Disadv
Advantages:Advantages:– Adapts to available main memoryAdapts to available main memory– Easily parallelizedEasily parallelized– Maximum number of database scans is Maximum number of database scans is
two.two. Disadvantages:Disadvantages:
– May have many candidates during second May have many candidates during second scan.scan.
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Parallelizing AR AlgorithmsParallelizing AR Algorithms
Based on AprioriBased on Apriori Techniques differ:Techniques differ:
– What is counted at each siteWhat is counted at each site– How data (transactions) are distributedHow data (transactions) are distributed
Data ParallelismData Parallelism– Data partitionedData partitioned– Count Distribution AlgorithmCount Distribution Algorithm
Task ParallelismTask Parallelism– Data and candidates partitionedData and candidates partitioned– Data Distribution AlgorithmData Distribution Algorithm
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Count Distribution Algorithm(CDA)Count Distribution Algorithm(CDA)1.1. Place data partition at each site.Place data partition at each site.2.2. In Parallel at each site doIn Parallel at each site do3.3. CC11 = Itemsets of size one in I; = Itemsets of size one in I;4.4. Count CCount C1;1;
5.5. Broadcast counts to all sites;Broadcast counts to all sites;6.6. Determine global large itemsets of size 1, LDetermine global large itemsets of size 1, L11;;7. i = 1; 8.8. RepeatRepeat9.9. i = i + 1;i = i + 1;10.10. CCi i = Apriori-Gen(L= Apriori-Gen(Li-1i-1););11.11. Count CCount Ci;i;
12.12. Broadcast counts to all sites;Broadcast counts to all sites;13.13. Determine global large itemsets of size i, LDetermine global large itemsets of size i, L ii;;14.14. until no more large itemsets found;until no more large itemsets found;
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CDA ExampleCDA Example
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Data Distribution Algorithm(DDA)Data Distribution Algorithm(DDA)1.1. Place data partition at each site.Place data partition at each site.2.2. In Parallel at each site doIn Parallel at each site do3.3. Determine local candidates of size 1 to count;Determine local candidates of size 1 to count;4.4. Broadcast local transactions to other sites;Broadcast local transactions to other sites;5.5. Count local candidates of size 1 on all data;Count local candidates of size 1 on all data;6.6. Determine large itemsets of size 1 for local Determine large itemsets of size 1 for local
candidates; candidates; 7.7. Broadcast large itemsets to all sites;Broadcast large itemsets to all sites;8.8. Determine LDetermine L11;;9. i = 1; 10.10. RepeatRepeat11.11. i = i + 1;i = i + 1;12.12. CCi i = Apriori-Gen(L= Apriori-Gen(Li-1i-1););13.13. Determine local candidates of size i to count;Determine local candidates of size i to count;14.14. Count, broadcast, and find LCount, broadcast, and find Lii;;15.15. until no more large itemsets found;until no more large itemsets found;
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DDA ExampleDDA Example
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Comparing AR TechniquesComparing AR Techniques TargetTarget TypeType Data TypeData Type Data SourceData Source TechniqueTechnique Itemset Strategy and Data StructureItemset Strategy and Data Structure Transaction Strategy and Data StructureTransaction Strategy and Data Structure OptimizationOptimization ArchitectureArchitecture Parallelism StrategyParallelism Strategy
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Comparison of AR TechniquesComparison of AR Techniques
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Hash TreeHash Tree
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Incremental Association RulesIncremental Association Rules Generate ARs in a dynamic database.Generate ARs in a dynamic database. Problem: algorithms assume static Problem: algorithms assume static
databasedatabase Objective: Objective:
– Know large itemsets for DKnow large itemsets for D– Find large itemsets for D Find large itemsets for D { { D} D}
Must be large in either D or Must be large in either D or D D Save LSave Li i and counts and counts
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Note on ARsNote on ARs Many applications outside market basket Many applications outside market basket
data analysisdata analysis– Prediction (telecom switch failure)Prediction (telecom switch failure)– Web usage miningWeb usage mining
Many different types of association rulesMany different types of association rules– TemporalTemporal– SpatialSpatial– CausalCausal
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Advanced AR TechniquesAdvanced AR Techniques
Generalized Association RulesGeneralized Association Rules Multiple-Level Association RulesMultiple-Level Association Rules Quantitative Association RulesQuantitative Association Rules Using multiple minimum supportsUsing multiple minimum supports Correlation RulesCorrelation Rules
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Measuring Quality of RulesMeasuring Quality of Rules
SupportSupport ConfidenceConfidence InterestInterest ConvictionConviction Chi Squared TestChi Squared Test
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Data Mining OutlineData Mining Outline
PART I - Introduction PART II – Core Topics
– Classification– Clustering– Association Rules
PART III – Related TopicsPART III – Related Topics
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Related Topics OutlineRelated Topics Outline
Database/OLTP SystemsDatabase/OLTP Systems Fuzzy Sets and LogicFuzzy Sets and Logic Information Retrieval(Web Search Engines)Information Retrieval(Web Search Engines) Dimensional ModelingDimensional Modeling Data WarehousingData Warehousing OLAP/DSSOLAP/DSS StatisticsStatistics Machine LearningMachine Learning Pattern MatchingPattern Matching
Goal:Goal: Examine some areas which are related to Examine some areas which are related to data mining.data mining.
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DB & OLTP SystemsDB & OLTP Systems SchemaSchema
– (ID,Name,Address,Salary,JobNo)(ID,Name,Address,Salary,JobNo) Data ModelData Model
– ERER– RelationalRelational
TransactionTransaction Query:Query:
SELECT NameSELECT NameFROM TFROM TWHERE Salary > 100000WHERE Salary > 100000
DM: Only imprecise queriesDM: Only imprecise queries
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Fuzzy Sets OutlineFuzzy Sets Outline
Introduction/OverviewIntroduction/Overview
Material for these slides obtained from:Material for these slides obtained from:
Data Mining Introductory and Advanced Topics by Margaret H. Dunham Data Mining Introductory and Advanced Topics by Margaret H. Dunham
http://www.engr.smu.edu/~mhd/bookIntroduction to “Type-2 Fuzzy Logic” by Jenny CarterIntroduction to “Type-2 Fuzzy Logic” by Jenny Carter
http://www.cse.dmu.ac.uk/~jennyc/
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Fuzzy Sets and LogicFuzzy Sets and Logic Fuzzy Set:Fuzzy Set: Set membership function is a real valued Set membership function is a real valued
function with output in the range [0,1].function with output in the range [0,1]. f(x): Probability x is in F.f(x): Probability x is in F. 1-f(x): Probability x is not in F.1-f(x): Probability x is not in F. EX:EX:
– T = {x | x is a person and x is tall}T = {x | x is a person and x is tall}– Let f(x) be the probability that x is tallLet f(x) be the probability that x is tall– Here f is the membership functionHere f is the membership function
DM: DM: Prediction and classification are fuzzy.Prediction and classification are fuzzy.
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Fuzzy Sets and LogicFuzzy Sets and Logic
Fuzzy Set:Fuzzy Set: Set membership function is a real Set membership function is a real valued function with output in the range [0,1].valued function with output in the range [0,1].
f(x): Probability x is in F.f(x): Probability x is in F. 1-f(x): Probability x is not in F.1-f(x): Probability x is not in F. EX:EX:
– T = {x | x is a person and x is tall}T = {x | x is a person and x is tall}– Let f(x) be the probability that x is tallLet f(x) be the probability that x is tall– Here f is the membership functionHere f is the membership function
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Fuzzy SetsFuzzy Sets
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IR is FuzzyIR is Fuzzy
Simple Fuzzy
Accept Accept
RejectReject
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Fuzzy Set TheoryFuzzy Set Theory
A fuzzy subset A of U is characterized by a A fuzzy subset A of U is characterized by a membership function membership function
(A,u) : U (A,u) : U [0,1] [0,1]which associates with each element which associates with each element uu of of
U a number U a number (u) in the interval [0,1](u) in the interval [0,1] DefinitionDefinition
– Let A and B be two fuzzy subsets of U. Also, let Let A and B be two fuzzy subsets of U. Also, let ¬A be the complement of A. Then,¬A be the complement of A. Then,
» (¬A,u) = 1 - (¬A,u) = 1 - (A,u) (A,u) » (A(AB,u) = max(B,u) = max((A,u), (A,u), (B,u))(B,u))» (A(AB,u) = min(B,u) = min((A,u), (A,u), (B,u))(B,u))
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The world is imprecise.The world is imprecise. Mathematical and Statistical techniques often Mathematical and Statistical techniques often
unsatisfactory.unsatisfactory.– Experts make decisions with imprecise data in an Experts make decisions with imprecise data in an
uncertain world.uncertain world.
– They work with knowledge that is rarely defined They work with knowledge that is rarely defined mathematically or algorithmically but uses vague mathematically or algorithmically but uses vague terminology with words.terminology with words.
Fuzzy logic is able to use vagueness to achieve Fuzzy logic is able to use vagueness to achieve a precise answer. By considering shades of grey a precise answer. By considering shades of grey and all factors simultaneously, you get a better and all factors simultaneously, you get a better answer, one that is more suited to the situation.answer, one that is more suited to the situation.
© Jenny Carter
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Fuzzy Logic then . . .Fuzzy Logic then . . . is particularly good at handling uncertainty, is particularly good at handling uncertainty,
vagueness and imprecision.vagueness and imprecision. especially useful where a problem can be especially useful where a problem can be
described linguistically (using words).described linguistically (using words). Applications include:Applications include:
– roboticsrobotics– washing machine controlwashing machine control– nuclear reactorsnuclear reactors– focusing a camcorderfocusing a camcorder– information retrievalinformation retrieval– train schedulingtrain scheduling
© Jenny Carter
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Crisp SetsCrisp Sets
Different heights have same ‘tallness’Different heights have same ‘tallness’
© Jenny Carter
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Fuzzy SetsFuzzy Sets
The shape you see is known as the membership The shape you see is known as the membership functionfunction
© Jenny Carter
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Fuzzy SetsFuzzy Sets
Shows two membership functions: ‘tall’ and ‘short’
© Jenny Carter
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NotationNotationFor the member, x, of a discrete set with membership µ we use the notation µ/x . In other words, x is a member of the set to degree µ. Discrete sets are written as:
A = µ1/x1 + µ2/x2 + .......... + µn/xn
Or
where x1, x2....xn are members of the set A and µ1, µ2, ...., µn are their degrees of membership. A continuous fuzzy set A is written as:
© Jenny Carter
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Fuzzy SetsFuzzy Sets The members of a fuzzy set are members to some The members of a fuzzy set are members to some
degree, known as a membership grade or degree degree, known as a membership grade or degree of membership.of membership.
The membership grade is the degree of belonging The membership grade is the degree of belonging to the fuzzy set. The larger the number (in [0,1]) to the fuzzy set. The larger the number (in [0,1]) the more the degree of belonging. (N.B. This is the more the degree of belonging. (N.B. This is notnot a probability)a probability)
The translation from x to µThe translation from x to µAA(x) is known as (x) is known as fuzzification.fuzzification.
A fuzzy set is either continuous or discrete.A fuzzy set is either continuous or discrete. Graphical representation of membership functions Graphical representation of membership functions
is very useful.is very useful.
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Fuzzy Sets - ExampleFuzzy Sets - Example
Again, notice the overlapping of the sets reflecting the real worldmore accurately than if we were using a traditional approach.
© Jenny Carter
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RulesRules Rules often of the form:Rules often of the form:
IF x is A THEN y is BIF x is A THEN y is B
where where A A and and B B are fuzzy sets defined on the are fuzzy sets defined on the universes of discourse universes of discourse X X and and Y Y respectively.respectively.
– if pressure is high then volume is small;if pressure is high then volume is small;– if a tomato is red then a tomato is ripe.if a tomato is red then a tomato is ripe.
where where high, small, redhigh, small, red and and riperipe are fuzzy sets. are fuzzy sets.
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Example - Dinner for twoExample - Dinner for two((p2-21 of FL toolbox user guide)p2-21 of FL toolbox user guide)
Rule 2 If service is good, then tip is average
Rule 3 If service is excellent or food is delicious, then tip is generous
The inputs are crisp (non-fuzzy) numbers limited to a specific range
All rules are evaluated in parallel using fuzzy reasoning
The results of the rules are combined and distilled (de-fuzzyfied)
The result is a crisp (non-fuzzy) number
Output
Tip (5-25%)
Dinner for two: this is a 2 input, 1 output, 3 rule system
Input 1
Service (0-10)
Input 2
Food (0-10)
Rule 1 If service is poor or food is rancid, then tip is cheap
© Jenny Carter
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Dinner for twoDinner for two
1.1. Fuzzify the Fuzzify the input:input:
2.2. Apply Fuzzy Apply Fuzzy operatoroperator
© Jenny Carter
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Dinner for twoDinner for two3. 3. Apply implication methodApply implication method
© Jenny Carter
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Dinner for twoDinner for two
4.4.
Aggregate Aggregate
all outputsall outputs
© Jenny Carter
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Dinner for twoDinner for two
5. 5. defuzzifydefuzzify
Various approaches e.g.
centre of area mean of max
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Information Retrieval Information Retrieval OutlineOutline
Introduction/OverviewIntroduction/Overview
Material for these slides obtained from:Material for these slides obtained from:Modern Information Retrieval by Ricardo Baeza-Yates and Berthier Ribeiro-Neto Modern Information Retrieval by Ricardo Baeza-Yates and Berthier Ribeiro-Neto
http://www.sims.berkeley.edu/~hearst/irbook/Data Mining Introductory and Advanced Topics by Margaret H. Dunham Data Mining Introductory and Advanced Topics by Margaret H. Dunham
http://www.engr.smu.edu/~mhd/book
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Information Retrieval Information Retrieval
Information Retrieval (IR):Information Retrieval (IR): retrieving desired retrieving desired information from textual data.information from textual data.
Library ScienceLibrary Science Digital LibrariesDigital Libraries Web Search EnginesWeb Search Engines Traditionally keyword basedTraditionally keyword based Sample query:Sample query:
Find all documents about “data mining”.Find all documents about “data mining”.
DM: Similarity measures; DM: Similarity measures; Mine text/Web data.Mine text/Web data.
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Information Retrieval Information Retrieval
Information Retrieval (IR):Information Retrieval (IR): retrieving desired retrieving desired information from textual data.information from textual data.
Library ScienceLibrary Science Digital LibrariesDigital Libraries Web Search EnginesWeb Search Engines Traditionally keyword basedTraditionally keyword based Sample query:Sample query:
Find all documents about “data mining”.Find all documents about “data mining”.
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DB vs IRDB vs IR
Records (tuples) vs. documentsRecords (tuples) vs. documents Well defined results vs. fuzzy resultsWell defined results vs. fuzzy results DB grew out of files and traditional DB grew out of files and traditional
business systesmbusiness systesm IR grew out of library science and need IR grew out of library science and need
to categorize/group/access to categorize/group/access books/articlesbooks/articles
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DB vs IR (cont’d)
Data retrievalwhich docs contain a set of keywords?Well defined semanticsa single erroneous object implies failure!
Information retrievalinformation about a subject or topicsemantics is frequently loosesmall errors are tolerated
IR system:interpret contents of information itemsgenerate a ranking which reflects relevancenotion of relevance is most important
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Motivation
IR in the last 20 years:classification and categorizationsystems and languagesuser interfaces and visualization
Still, area was seen as of narrow interestAdvent of the Web changed this perception once and for all
universal repository of knowledge free (low cost) universal accessno central editorial boardmany problems though: IR seen as key to finding the solutions!
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Basic Concepts
Logical view of the documents
Document representation viewed as a continuum: logical view of docs might shift
structure
Accentsspacing stopwords
Noungroups stemming
Manual indexingDocs
structure Full text Index terms
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UserInterface
Text Operations
Query Operations Indexing
Searching
Ranking
Index
Text
query
user need
user feedback
ranked docs
retrieved docs
logical viewlogical view
inverted file
DB Manager Module
Text Database
Text
The Retrieval Process
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Information Retrieval Information Retrieval
Similarity:Similarity: measure of how close a query is measure of how close a query is to a document.to a document.
Documents which are “close enough” are Documents which are “close enough” are retrieved.retrieved.
Metrics:Metrics:– PrecisionPrecision = |Relevant and Retrieved| = |Relevant and Retrieved|
|Retrieved||Retrieved|– RecallRecall = |Relevant and Retrieved|= |Relevant and Retrieved|
|Relevant||Relevant|
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IndexingIndexing
IR systems usually adopt index terms to IR systems usually adopt index terms to process queriesprocess queries
Index term:Index term:– a keyword or group of selected wordsa keyword or group of selected words– any word (more general)any word (more general)
Stemming might be used:Stemming might be used:– connect: connecting, connection, connectionsconnect: connecting, connection, connections
An inverted file is built for the chosen index An inverted file is built for the chosen index termsterms
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Indexing Indexing Docs
Information Need
Index Terms
doc
query
Rankingmatch
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Inverted FilesInverted Files There are two main elements: There are two main elements:
– vocabulary – set of unique terms vocabulary – set of unique terms – Occurrences – where those terms appear Occurrences – where those terms appear
The occurrences can be recorded as The occurrences can be recorded as terms or byte offsetsterms or byte offsets
Using term offset is good to retrieve Using term offset is good to retrieve concepts such as proximity, whereas concepts such as proximity, whereas byte offsets allow direct accessbyte offsets allow direct access
VocabularyVocabulary Occurrences (byte offset)Occurrences (byte offset)
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Inverted FilesInverted Files
The number of indexed terms is often several The number of indexed terms is often several orders of magnitude smaller when compared orders of magnitude smaller when compared to the documents size (Mbs vs Gbs)to the documents size (Mbs vs Gbs)
The space consumed by the occurrence list is The space consumed by the occurrence list is not trivial. Each time the term appears it must not trivial. Each time the term appears it must be added to a list in the inverted filebe added to a list in the inverted file
That may lead to a quite considerable index That may lead to a quite considerable index overheadoverhead
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ExampleExample Text: Text:
Inverted fileInverted file
1 6 12 16 18 25 29 36 40 45 54 58 66 70
That house has a garden. The garden has many flowers. The flowers are beautiful
beautiful
flowers
garden
house
70
45, 58
18, 29
6
Vocabulary Occurrences
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RankingRanking
A A rankingranking is an ordering of the documents is an ordering of the documents retrieved that (hopefully) reflects the retrieved that (hopefully) reflects the relevance of the documents to the query relevance of the documents to the query
A ranking is based on fundamental A ranking is based on fundamental premisses regarding the notion of relevance, premisses regarding the notion of relevance, such as:such as:– common sets of index termscommon sets of index terms– sharing of weighted termssharing of weighted terms– likelihood of relevancelikelihood of relevance
Each set of premisses leads to a distinct Each set of premisses leads to a distinct IR modelIR model© Baeza-Yates and Ribeiro-NetoBaeza-Yates and Ribeiro-Neto
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Classic IR Models - Basic ConceptsClassic IR Models - Basic Concepts
Each document represented by a set of Each document represented by a set of representative keywords or index termsrepresentative keywords or index terms
An index term is a document word useful for An index term is a document word useful for remembering the document main themesremembering the document main themes
Usually, index terms are nouns because Usually, index terms are nouns because nouns have meaning by themselvesnouns have meaning by themselves
However, search engines assume that all However, search engines assume that all words are index terms (full text words are index terms (full text representation)representation)
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Classic IR Models - Basic ConceptsClassic IR Models - Basic Concepts
The The importanceimportance of the index terms is of the index terms is represented by weights associated to represented by weights associated to themthem
kkii- an index term- an index term
ddjj - a document - a document
wwij ij - a weight associated with - a weight associated with (k(kii,d,djj))
The weight The weight wwijij quantifies the importance of quantifies the importance of
the index term for describing the document the index term for describing the document contentscontents
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Classic IR Models - Basic ConceptsClassic IR Models - Basic Concepts
– t t is the total number of index termsis the total number of index terms– K = {kK = {k11, k, k22, …, k, …, ktt} } is the set of all index termsis the set of all index terms
– wwij ij >= 0 >= 0 is a weight associated with is a weight associated with (k(kii,d,djj))
– wwijij = 0 = 0 indicates that term does not belong indicates that term does not belong
to docto doc– ddjj= (w= (w1j1j, w, w2j2j, …, w, …, wtjtj) ) is a weighted vector is a weighted vector
associated with the document associated with the document ddjj
– ggii(d(djj) = w) = wij ij is a function which returns the is a function which returns the
weight associated with pair weight associated with pair (k(kii,d,djj))
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The Boolean ModelThe Boolean Model
Simple model based on set theorySimple model based on set theory Queries specified as boolean expressions Queries specified as boolean expressions
– precise semantics and neat formalismprecise semantics and neat formalism Terms are either present or absent. Thus, Terms are either present or absent. Thus,
wwij ij {0,1} {0,1} ConsiderConsider
– q = kq = ka a (k(kb b kkcc))
– qqdnf dnf = (1,1,1) = (1,1,1) (1,1,0) (1,1,0) (1,0,0)(1,0,0)
– qqcccc= (1,1,0) = (1,1,0) is a conjunctive componentis a conjunctive component© Baeza-Yates and Ribeiro-NetoBaeza-Yates and Ribeiro-Neto
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The Vector ModelThe Vector Model
Use of binary weights is too limitingUse of binary weights is too limiting Non-binary weights provide consideration for Non-binary weights provide consideration for
partial matchespartial matches These term weights are used to compute a These term weights are used to compute a
degree of similaritydegree of similarity between a query and between a query and each documenteach document
Ranked set of documents provides for better Ranked set of documents provides for better matchingmatching
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The Vector ModelThe Vector Model
wwij ij > 0 > 0 whenever whenever kki i appears in d appears in djj
wwiqiq >= 0 >= 0 associated with the pair associated with the pair (k(kii,q),q)
ddj j = (w= (w1j1j, w, w2j2j, ..., w, ..., wtjtj))
q = (wq = (w1q1q, w, w2q2q, ..., w, ..., wtqtq))
To each term To each term kki i is associated a unitary vectoris associated a unitary vector i i The unitary vectors The unitary vectors i i andand j j are assumed to be are assumed to be
orthonormal (i.e., index terms are assumed to orthonormal (i.e., index terms are assumed to occur independently within the documents)occur independently within the documents)
The The tt unitary vectors unitary vectors ii form an orthonormal basis form an orthonormal basis for a t-dimensional space where queries and for a t-dimensional space where queries and documents are represented as weighted vectors documents are represented as weighted vectors © Baeza-Yates and Ribeiro-NetoBaeza-Yates and Ribeiro-Neto
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Query Languages Query Languages
Keyword BasedKeyword Based BooleanBoolean Weighted BooleanWeighted Boolean Context Based (Phrasal & Proximity)Context Based (Phrasal & Proximity) Pattern MatchingPattern Matching Structural QueriesStructural Queries
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Keyword Based QueriesKeyword Based Queries
Basic QueriesBasic Queries– Single wordSingle word– Multiple wordsMultiple words
Context QueriesContext Queries– PhrasePhrase– ProximityProximity
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Boolean QueriesBoolean Queries
Keywords combined with Boolean operators:Keywords combined with Boolean operators:– OR: (OR: (ee11 OR OR ee22))
– AND: (AND: (ee11 AND AND ee22))
– BUT: (BUT: (ee11 BUT BUT ee22) Satisfy ) Satisfy ee11 but but notnot ee22
Negation only allowed using BUT to allow Negation only allowed using BUT to allow efficient use of inverted index by filtering efficient use of inverted index by filtering another efficiently retrievable set.another efficiently retrievable set.
Naïve users have trouble with Boolean logic.Naïve users have trouble with Boolean logic.
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Boolean Retrieval with Inverted IndicesBoolean Retrieval with Inverted Indices
Primitive keywordPrimitive keyword: Retrieve containing : Retrieve containing documents using the inverted index.documents using the inverted index.
OROR: Recursively retrieve : Recursively retrieve ee11 and and ee22 and and take union of results.take union of results.
ANDAND: Recursively retrieve : Recursively retrieve ee11 and and ee22 and and take intersection of results.take intersection of results.
BUTBUT: Recursively retrieve : Recursively retrieve ee11 and and ee22 and and take set difference of results.take set difference of results.
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Phrasal QueriesPhrasal Queries
Retrieve documents with a specific phrase Retrieve documents with a specific phrase (ordered list of contiguous words)(ordered list of contiguous words)– ““information theory”information theory”
May allow intervening stop words and/or May allow intervening stop words and/or stemming.stemming.– ““buy camera” matches: buy camera” matches:
““buy a camera” buy a camera” “buying the cameras” “buying the cameras” etc. etc.
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Phrasal Retrieval with Inverted IndicesPhrasal Retrieval with Inverted Indices
Must have an inverted index that also stores Must have an inverted index that also stores positionspositions of each keyword in a document. of each keyword in a document.
Retrieve documents and positions for each Retrieve documents and positions for each individual word, intersect documents, and individual word, intersect documents, and then finally check for ordered contiguity of then finally check for ordered contiguity of keyword positions.keyword positions.
Best to start contiguity check with the least Best to start contiguity check with the least common word in the phrase.common word in the phrase.
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Proximity QueriesProximity Queries
List of words with specific maximal List of words with specific maximal distance constraints between terms.distance constraints between terms.
Example: “dogs” and “race” within 4 Example: “dogs” and “race” within 4 words match “…dogs will begin words match “…dogs will begin the race…”the race…”
May also perform stemming and/or not May also perform stemming and/or not count stop words.count stop words.
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Pattern MatchingPattern Matching
Allow queries that match strings rather Allow queries that match strings rather than word tokens.than word tokens.
Requires more sophisticated data Requires more sophisticated data structures and algorithms than inverted structures and algorithms than inverted indices to retrieve efficiently. indices to retrieve efficiently.
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Simple PatternsSimple Patterns
PrefixesPrefixes: Pattern that matches start of word.: Pattern that matches start of word.– ““anti” matches “antiquity”, “antibody”, etc.anti” matches “antiquity”, “antibody”, etc.
SuffixesSuffixes: Pattern that matches end of word:: Pattern that matches end of word:– ““ix” matches “fix”, “matrix”, etc.ix” matches “fix”, “matrix”, etc.
SubstringsSubstrings: Pattern that matches arbitrary : Pattern that matches arbitrary subsequence of characters.subsequence of characters.– “ “rapt” matches “enrapture”, “velociraptor” etc.rapt” matches “enrapture”, “velociraptor” etc.
RangesRanges: Pair of strings that matches any word : Pair of strings that matches any word lexicographically (alphabetically) between lexicographically (alphabetically) between them.them.– ““tin” to “tix” matches “tip”, “tire”, “title”, etc.tin” to “tix” matches “tip”, “tire”, “title”, etc.
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IR Query Result Measures IR Query Result Measures and Classificationand Classification
IR Classification
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Dimensional ModelingDimensional Modeling View data in a hierarchical manner more as View data in a hierarchical manner more as
business executives mightbusiness executives might Useful in decision support systems and miningUseful in decision support systems and mining Dimension:Dimension: collection of logically related collection of logically related
attributes; axis for modeling data.attributes; axis for modeling data. Facts:Facts: data stored data stored Ex: Dimensions – products, locations, dateEx: Dimensions – products, locations, date
Facts – quantity, unit priceFacts – quantity, unit price
DM: May view data as dimensional.DM: May view data as dimensional.
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Dimensional ModelingDimensional Modeling
View data in a hierarchical manner more as View data in a hierarchical manner more as business executives mightbusiness executives might
Useful in decision support systems and miningUseful in decision support systems and mining Dimension:Dimension: collection of logically related collection of logically related
attributes; axis for modeling data.attributes; axis for modeling data. Facts:Facts: data stored data stored Ex: Dimensions – products, locations, dateEx: Dimensions – products, locations, date
Facts – quantity, unit priceFacts – quantity, unit price
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Aggregation HierarchiesAggregation Hierarchies
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Multidimensional SchemasMultidimensional Schemas
Star Schema shows facts and dimensionsStar Schema shows facts and dimensions– Center of the star has facts shown in fact tablesCenter of the star has facts shown in fact tables– Outside of the facts, each diemnsion is shown Outside of the facts, each diemnsion is shown
separately in dimension tablesseparately in dimension tables– Access to fact table from dimension table via joinAccess to fact table from dimension table via join
SELECT Quantity, PriceSELECT Quantity, PriceFROM Facts, LocationFROM Facts, LocationWhere (Facts.LocationID = Location.LocationID) andWhere (Facts.LocationID = Location.LocationID) and(Location.City = ‘Dallas’)(Location.City = ‘Dallas’)
– View as relations, problem volume of data and View as relations, problem volume of data and indexingindexing
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Star SchemaStar Schema
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Flattened StarFlattened Star
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Normalized StarNormalized Star
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Snowflake SchemaSnowflake Schema
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OLAPOLAP Online Analytic Processing (OLAP):Online Analytic Processing (OLAP): provides more provides more
complex queries than OLTP.complex queries than OLTP. OnLine Transaction Processing (OLTP):OnLine Transaction Processing (OLTP): traditional traditional
database/transaction processing.database/transaction processing. Dimensional data; cube view Dimensional data; cube view Visualization of operations:Visualization of operations:
– Slice:Slice: examine sub-cube. examine sub-cube.– Dice:Dice: rotate cube to look at another dimension. rotate cube to look at another dimension.– Roll Up/Drill DownRoll Up/Drill Down
DM: May use OLAP queries.DM: May use OLAP queries.
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OLAP IntroductionOLAP Introduction
OLAP by ExampleOLAP by Example
http://perso.orange.fr/bernard.lupin/english/index.htm What is OLAP?What is OLAP?
http://www.olapreport.com/fasmi.htm
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OLAPOLAP Online Analytic Processing (OLAP):Online Analytic Processing (OLAP): provides more provides more
complex queries than OLTP.complex queries than OLTP. OnLine Transaction Processing (OLTP):OnLine Transaction Processing (OLTP): traditional traditional
database/transaction processing.database/transaction processing. Dimensional data; cube view Dimensional data; cube view Support ad hoc queryingSupport ad hoc querying Require analysis of dataRequire analysis of data Can be thought of as an extension of some of the basic Can be thought of as an extension of some of the basic
aggregation functions available in SQLaggregation functions available in SQL OLAP tools may be used in DSS systemsOLAP tools may be used in DSS systems Multidimentional view is fundamentalMultidimentional view is fundamental
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OLAP ImplementationsOLAP Implementations MOLAP (Multidimensional OLAP)MOLAP (Multidimensional OLAP)
– Multidimential Database (MDD)Multidimential Database (MDD)– Specialized DBMS and software system capable of supporting Specialized DBMS and software system capable of supporting
the multidimensional data directlythe multidimensional data directly– Data stored as an n-dimensional array (cube)Data stored as an n-dimensional array (cube)– Indexes used to speed up processingIndexes used to speed up processing
ROLAP (Relational OLAP)ROLAP (Relational OLAP)– Data stored in a relational databaseData stored in a relational database– ROLAP server (middleware) creates the multidimensional view ROLAP server (middleware) creates the multidimensional view
for the userfor the user– Less Complex; Less efficientLess Complex; Less efficient
HOLAP (Hybrid OLAP)HOLAP (Hybrid OLAP)– Not updated frequently – MDDNot updated frequently – MDD– Updated frequently - RDBUpdated frequently - RDB
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OLAP OperationsOLAP Operations
Single Cell Multiple Cells Slice Dice
Roll Up
Drill Down
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OLAP OperationsOLAP Operations
Simple query – single cell in the cubeSimple query – single cell in the cube SliceSlice – Look at a subcube to get more – Look at a subcube to get more
specific informationspecific information Dice Dice – Rotate cube to look at another – Rotate cube to look at another
dimensiondimension Roll UpRoll Up – Dimension Reduction; Aggregation – Dimension Reduction; Aggregation Drill DownDrill Down Visualization: These operations allow the Visualization: These operations allow the
OLAP users to actually “see” results of an OLAP users to actually “see” results of an operation.operation.
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Relationship Between TopcsRelationship Between Topcs
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Decision Support SystemsDecision Support Systems Tools and computer systems that assist Tools and computer systems that assist
management in decision makingmanagement in decision making What if types of questionsWhat if types of questions High level decisionsHigh level decisions Data warehouse – data which supports Data warehouse – data which supports
DSSDSS
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Unified Dimensional ModelUnified Dimensional Model
Microsoft Cube ViewMicrosoft Cube View SQL Server 2005SQL Server 2005
http://msdn2.microsoft.com/en-us/library/ms345143.aspx
http://cwebbbi.spaces.live.com/Blog/cns!1pi7ETChsJ1un_2s41jm9Iyg!325.entry MDX AS2005MDX AS2005
http://msdn2.microsoft.com/en-us/library/aa216767(SQL.80).aspx
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Data WarehousingData Warehousing
““Subject-oriented, integrated, time-variant, nonvolatile” Subject-oriented, integrated, time-variant, nonvolatile” William InmonWilliam Inmon
Operational Data:Operational Data: Data used in day to day needs of Data used in day to day needs of company.company.
Informational Data:Informational Data: Supports other functions such as Supports other functions such as planning and forecasting.planning and forecasting.
Data mining tools often access data warehouses rather Data mining tools often access data warehouses rather than operational data.than operational data.
DM: May access data in warehouse.DM: May access data in warehouse.
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Operational vs. InformationalOperational vs. Informational
Operational Data Data Warehouse
Application OLTP OLAP
Use Precise Queries Ad Hoc
Temporal Snapshot Historical
Modification Dynamic Static
Orientation Application Business
Data Operational Values Integrated
Size Gigabits TerabitsLevel Detailed Summarized
Access Often Less Often
Response Few Seconds Minutes
Data Schema Relational Star/Snowflake
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StatisticsStatistics Simple descriptive modelsSimple descriptive models Statistical inference:Statistical inference: generalizing a model generalizing a model
created from a sample of the data to the entire created from a sample of the data to the entire dataset.dataset.
Exploratory Data Analysis:Exploratory Data Analysis: – Data can actually drive the creation of the Data can actually drive the creation of the
modelmodel– Opposite of traditional statistical view.Opposite of traditional statistical view.
Data mining targeted to business userData mining targeted to business user
DM: Many data mining methods come DM: Many data mining methods come from statistical techniques. from statistical techniques.
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Machine Learning Outline Machine Learning Outline
Introduction (Chuck Anderson)Introduction (Chuck Anderson)
CS545: Machine LearningCS545: Machine Learning
By Chuck AndersonBy Chuck Anderson
Department of Computer ScienceDepartment of Computer Science
Colorado State UniversityColorado State University
Fall 2006Fall 2006
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Machine LearningMachine Learning Machine Learning:Machine Learning: area of AI that examines how to area of AI that examines how to
write programs that can learn.write programs that can learn. Often used in classification and prediction Often used in classification and prediction Supervised Learning:Supervised Learning: learns by example. learns by example. Unsupervised Learning: Unsupervised Learning: learns without knowledge of learns without knowledge of
correct answers.correct answers. Machine learning often deals with small static datasets. Machine learning often deals with small static datasets.
DM: Uses many machine learning DM: Uses many machine learning techniques.techniques.
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What is Machine Learning?
Statistics ≈ the science of inference from data Machine learning ≈ multivariate statistics +
computational statistics Multivariate statistics ≈ prediction of values of
a function assumed to underlie a multivariate dataset
Computational statistics ≈ computational methods for statistical problems (aka statistical computation) + statistical methods which happen to be computationally intensive
Data Mining ≈ exploratory data analysis, particularly with massive/complex datasets
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Kinds of Learning Learning algorithms are often categorized
according to the amount of information provided:
Least Information:– Unsupervised learning is more exploratory.– Requires samples of inputs. Must find regularities.
More Information:– Reinforcement learning most recent.– Requires samples of inputs, actions, and rewards
or punishments. Most Information:
– Supervised learning is most common.– Requires samples of inputs and desired outputs.
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Examples of Algorithms
Supervised learning– Regression
» multivariate regression» neural networks and kernel methods
– Classification» linear and quadratic discrimination analysis» k-nearest neighbors» neural networks and kernel methods
Reinforcement learning– multivariate regression– neural networks
Unsupervised learning– principal components analysis– k-means clustering– self-organizing networks
© Chuck AndersonChuck Anderson
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Pattern Matching Pattern Matching (Recognition)(Recognition)
Pattern Matching:Pattern Matching: finds occurrences of finds occurrences of a predefined pattern in the data.a predefined pattern in the data.
Applications include speech recognition, Applications include speech recognition, information retrieval, time series information retrieval, time series analysis.analysis.
DM: Type of classification.DM: Type of classification.
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Image Mining OutlineImage Mining Outline
Image Mining – What is it?Image Mining – What is it? Feature ExtractionFeature Extraction Shape DetectionShape Detection Color TechniquesColor Techniques Video MiningVideo Mining Facial RecognitionFacial Recognition BioinformaticsBioinformatics
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The 2000 ozone hole over the antarctic seen by EPTOMS http://jwocky.gsfc.nasa.gov/multi/multi.html#hole
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Image Mining – What is it?Image Mining – What is it? Image RetrievalImage Retrieval Image ClassificationImage Classification Image ClusteringImage Clustering Video MiningVideo Mining Applications Applications
– BioinformaticsBioinformatics– Geology/Earth ScienceGeology/Earth Science– SecuritySecurity– ……
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Feature ExtractionFeature Extraction
Identify major components of imageIdentify major components of image ColorColor TextureTexture ShapeShape Spatial relationshipsSpatial relationships Feature Extraction & Image ProcessingFeature Extraction & Image Processing
http://users.ecs.soton.ac.uk/msn/book/ Feature Extraction TutorialFeature Extraction Tutorial
http://facweb.cs.depaul.edu/research/vc/VC_Workshop/presentations/pdf/daniela_tutorial2.pdf
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Shape DetectionShape Detection
Boundary/Edge DetectionBoundary/Edge Detection Time Series – Eamonn KeoghTime Series – Eamonn Keogh
http://www.engr.smu.edu/~mhd/8337sp07/shapes.ppt
330CSE 5331/7331 F'09
Color TechniquesColor Techniques
Color RepresentationsColor Representations
RGB:RGB:
http://en.wikipedia.org/wiki/Rgb
HSV: HSV: http://en.wikipedia.org/wiki/HSV_color_space
Color HistogramColor Histogram Color AnglogramColor Anglogram
http://www.cs.sunysb.edu/~rzhao/publications/VideoDB.pdf
331CSE 5331/7331 F'09
What is SimilarityWhat is Similarity??
(c) Eamonn Keogh, eamonn@cs.ucr.edu
332CSE 5331/7331 F'09
Video MiningVideo Mining
Boundaries between shotsBoundaries between shots Movement between framesMovement between frames ANSES:ANSES:
http://mmir.doc.ic.ac.uk/demos/anses.html
333CSE 5331/7331 F'09
Facial RecognitionFacial Recognition Based upon features in faceBased upon features in face Convert face to a feature vectorConvert face to a feature vector Less invasive than other biometric techniquesLess invasive than other biometric techniques http://www.face-rec.org http://computer.howstuffworks.com/facial-recogniti
on.htm SIMS: SIMS:
http://www.casinoincidentreporting.com/Products.aspx
334CSE 5331/7331 F'09
Microarray Data Microarray Data AnalysisAnalysis
Each probe location associated with geneEach probe location associated with gene Measure the amount of mRNAMeasure the amount of mRNA Color indicates degree of gene expressionColor indicates degree of gene expression Compare different samples (normal/disease)Compare different samples (normal/disease) Track same sample over timeTrack same sample over time QuestionsQuestions
– Which genes are related to this disease?Which genes are related to this disease?– Which genes behave in a similar manner?Which genes behave in a similar manner?– What is the function of a gene?What is the function of a gene?
ClusteringClustering– HierarchicalHierarchical– K-meansK-means
335CSE 5331/7331 F'09
Affymetrix GeneChipAffymetrix GeneChip®® ArrayArray
http://www.affymetrix.com/corporate/outreach/lesson_plan/educator_resources.affx
336CSE 5331/7331 F'09
Microarray Data - Microarray Data - ClusteringClustering
"Gene expression profiling identifies clinically relevant subtypes of prostate cancer"
Proc. Natl. Acad. Sci. USA, Vol. 101, Issue 3, 811-816, January 20, 2004
337CSE 5331/7331 F'09
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