clustering and segmentation
DESCRIPTION
Clustering and segmentation. MIS2502 Data Analytics Adapted from Tan, Steinbach, and Kumar (2004). Introduction to Data Mining . http://www-users.cs.umn.edu/~kumar/dmbook/. What is Cluster Analysis?. Grouping data so that elements in a group will be Similar (or related) to one another - PowerPoint PPT PresentationTRANSCRIPT
CLUSTERING AND SEGMENTATIONMIS2502
Data Analytics
Adapted from Tan, Steinbach, and Kumar (2004). Introduction to Data Mining.http://www-users.cs.umn.edu/~kumar/dmbook/
What is Cluster Analysis?• Grouping data so that elements in a group will be
• Similar (or related) to one another• Different (or unrelated) from elements in other groups
http://www.baseball.bornbybits.com/blog/uploaded_images/Takashi_Saito-703616.gif
Distance within clusters is minimized
Distance between
clusters is maximized
Applications
Understanding• Group related documents for browsing• Create groups of similar customers• Discover which stocks have similar price
fluctuations
Summarization• Reduce the size of large data sets• Those similar groups can be treated as a
single data point
Even more examples
Marketing• Discover distinct customer groups for
targeted promotions
Insurance• Finding “good customers” (low claim costs,
reliable premium payments)
Healthcare• Find patients with high-risk behaviors
What cluster analysis is NOT
Manual (“supervised”) classification• People simply place items into
categories
Simple segmentation
• Dividing students into groups by last name
Main idea:
The clusters must come from the data, not from
external specifications.
Creating the “buckets”
beforehand is categorization, but
not clustering.
Clusters can be ambiguous
The difference is the threshold you set.How distinct must a cluster be to be it’s own cluster?
How many clusters? 6
2 4
Two clustering techniques
Partition• Non-overlapping
subsets (clusters) such that each data object is in exactly one subset
Hierarchical• Set of nested clusters
organized as a hierarchical tree
Partitional Clustering
Three distinct groups emerge,
but…
…some curveballs behave more like
splitters.
…some splitters look more like
fastballs.
Hierarchical Clustering
p1
p2
p3
p5
p4
p1 p2 p3 p4 p5
This is a dendrogram
Tree diagram used to represent
clusters
Clusters can be ambiguous
The difference is the threshold you set.How distinct must a cluster be to be it’s own cluster?
How many clusters? 6
2 4
adapted from Tan, Steinbach, and Kumar. Introduction to Data Mining (2004)
K-means (partitional)
Choose K clusters
Select K points as initial centroids
Assign all points to clusters based on distance
Recompute the centroid of each cluster
Did the center change? DONE!
Yes
No
The K-means algorithm is one
method for doing partitional
clustering
K-Means Demonstration
Here is the initial data set
K-Means Demonstration
Choose K points as
initial centroids
K-Means Demonstration
Assign data points
according to distance
K-Means Demonstration
And re-assign the points
K-Means Demonstration
Recalculate the centroids
K-Means Demonstration
And keep doing that until you
settle on a final set of
clusters
Choosing the initial centroids
• Choosing the right number• Choosing the right initial location
It matters
• They won’t make sense within the context of the problem
• Unrelated data points will be included in the same group
Bad choices create bad groupings
Example of Poor Initialization
This may “work” mathematically but the clusters don’t make much sense.
Evaluating K-Means Clusters• On the previous slide, we did it visually, but there is a
mathematical test
• Sum-of-Squares Error (SSE)• The distance to the nearest cluster center• How close does each point get to the center?
• This just means• In a cluster, compute distance from a point (m) to the cluster center (x)• Square that distance (so sign isn’t an issue)• Add them all together
K
i Cxi
i
xmdistSSE1
2 ),(
Example: Evaluating ClustersCluster 1 Cluster 2
2
1.313 3.3
1.5
SSE1 = 12 + 1.32 + 22 = 1 + 1.69 + 4 = 6.69
SSE2 = 32 + 3.32 + 1.52 = 9 + 10.89 + 2.25 = 22.14
• Lower individual cluster SSE = a better cluster• Lower total SSE = a better set of clusters• More clusters will reduce SSE
Considerations Reducing SSE within a cluster
increases cohesion(we want that)
Choosing the best initial centroids• There’s no single, best way to choose initial centroids
• So what do you do?• Multiple runs (?)• Use a sample set of data first
• And then apply it to your main data set
• Select more centroids to start with• Then choose the ones that are farthest apart• Because those are the most distinct
• Pre and post-processing of the data
Pre-processing: Getting the right centroids
• “Pre” Get the data ready for analysis
• Normalize the data• Reduces the dispersion of data points by re-computing the
distance• Rationale: Preserves differences while dampening the effect of the
outliers
• Remove outliers • Reduces the dispersion of data points by removing the atypical
data• Rationale: They don’t represent the population anyway
Post-processing: Getting the right centroids
• “Post” Interpreting the results of the clustering analysis
• Remove small clusters• May be outliers
• Split loose clusters• With high SSE that look like they are really two different groups
• Merge clusters• With relatively low SSE that are “close” together
Limitations of K-Means Clustering
• Clusters vary widely in size• Clusters vary widely in density• Clusters are not in rounded
shapes• The data set has a lot of outliers
K-Means gives
unreliable results when
The clusters may never make sense.In that case, the data may just not be well-suited for clustering!
Similarity between clusters (inter-cluster)
• Most common: distance between centroids• Also can use SSE
• Look at distance between cluster 1’s points and other centroids• You’d want to maximize SSE between clusters
Cluster 1
Cluster 5
Increasing SSE across
clusters increases
separation(we want that)
Figuring out if our clusters are good• “Good” means
• Meaningful• Useful• Provides insight
• The pitfalls• Poor clusters reveal incorrect associations• Poor clusters reveal inconclusive associations• There might be room for improvement and we can’t tell
• This is somewhat subjective and depends upon the expectations of the analyst
Cluster validity assessment
• Do to the clusters confirm predefined labels?
• i.e., “Entropy”External
• How well-formed are the clusters?• i.e., SSE or correlationInternal
• How well does one clustering algorithm compare to another?
• i.e., compare SSEsRelative
The Keys to Successful Clustering
• We want high cohesion within clusters (minimize differences)• High SSE, high correlation
• And high separation between clusters (maximize differences)• Low SSE, low correlation
• We need to choose the right number of clusters
• We need to choose the right initial centroids
• But there’s no easy way to do this• Combination of trial-and-error, knowledge of
the problem, and looking at the output
In SAS, cohesion is measured by root mean
square standard deviation…
…and separation measured by distance to
nearest cluster