dmtm 2015 - 04 data exploration

Prof. Pier Luca Lanzi

Data Exploration !Data Mining and Text Mining (UIC 583 @ Politecnico di Milano)


Readings

•  “Data Mining and Analysis” – Chapter 2 & 3

•  Loading Data and Basic Formatting in R !http://flowingdata.com/2015/02/18/loading-data-and-basic-formatting-in-r/

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before trying anything, you should know your data!


What is Data Exploration?

•  It is the preliminary exploration of the data aimed at identifying their most relevant characteristics

• What the key motivations?! Helping to select the right tool for preprocessing and data

mining ! Exploiting humans’ abilities to recognize patterns !

not captured by automatic tools •  Related to Exploratory Data Analysis (EDA), created by

statistician John Tukey

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Exploratory Data Analysis

•  “An approach of analyzing data to summarize their main characteristics without using a statistical model or having formulated a prior hypothesis.”

•  “Exploratory data analysis was promoted by John Tukey to encourage statisticians to explore the data, and possibly formulate hypotheses that could lead to new data collection and experiments.”!

•  Seminal book is “Exploratory Data Analysis” by Tukey

•  Nice online introduction in Chapter 1 of the NIST Engineering Statistics Handbook !http://www.itl.nist.gov/div898/handbook/index.htm

•  http://en.wikipedia.org/wiki/Exploratory_data_analysis!

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http://vis.stanford.edu/files/2012-EnterpriseAnalysisInterviews-VAST.pdf


What Data Exploration Techniques?

•  Exploratory Data Analysis (as originally defined by Tukey),!was mainly focused on! Visualization! Clustering and anomaly detection !

(viewed as exploratory techniques)! In data mining, clustering and anomaly detection are major

areas of interest, and not thought of as just exploratory•  In this section, we focus on data exploration using! Summary statistics! Visualization

• We will come back later to data exploration when discussing clustering

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numerical attributes


Geometric Interpretation of Correlation

•  The correlation coefficient is simply the cosine of the angle between the two centered attribute vectors

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normalization


Summary Statistics

•  They are numbers that summarize properties of the data

•  Summarized properties include location, mean, spread, skewness, standard deviation

•  Most summary statistics can be calculated in a single pass

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Frequency and Mode

•  The frequency of an attribute value is the percentage of time the value occurs in the data set

•  For example, given the attribute ‘gender’ and a representative population of people, the gender ‘female’ occurs about 50% of the time.

•  The mode of an attribute is the most frequent attribute value

•  The notions of frequency and mode are typically used with categorical data

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Measures of Location:!Mean and Median

•  The mean is the most common measure of the location of a set of points

•  However, the mean is very sensitive to outliers

•  Thus, the median or a trimmed mean is also commonly used

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Measures of Spread: !Range and Variance

•  Range is the difference between the max and min•  The variance or standard deviation is the most common measure

of the spread of a set of points

•  However, this is also sensitive to outliers, so that other measures are often used

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Percentiles

•  For continuous data, the notion of a percentile is veryuseful

•  Given an ordinal or continuous attribute x and a number p between 0 and 100, the p-th percentile is a value xp of x such that p% of the observed values of x are less than xp

•  For instance, the 50th percentile is the value x50% such that 50% of all values of x are less than x50%

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Summary Statistics in R

# stringr is also needed to be installed # required libraries library(foreign) library(rattle) library(plyr) # set working directory setwd("~/Dropbox/Documents/Online/Corsi/DMTM/data") # load data wnum = read.arff("weather.numeric.arff") # check the structure str(wnum) # names of the attributes names(wnum) # rename the attributes to normalize them in lowercase names <- normVarNames(names(wnum))

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# summary statistics summary(wnum) mean(wnum$humidity) sd(wnum$humidity) var(wnum$humidity) median(wnum$humidity) max(wnum$humidity) min(wnum$humidity) # first ten rows head(wnum,10) # first 5 rows columns 1 & 3 head(wnum[c(1,3)],5) # naming the columns head(wnum[c("humidity", "temperature")])

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# sampling ten rows head(wnum[sample(nrow(wnum), 10),c("humidity", "temperature")]) # selecting the rows based an attribute properties wnum[wnum$outlook=="sunny",] # exploring data with sorted attributes wnum[order(wnum$temperature),] ### ### grouping and summarizing data ### ddply(snum,"outlook",summarize, max=max(temperature, na.rm=TRUE))

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Visualization

•  Visualization is the conversion of data into a visual or tabular format so that the characteristics of the data and the relationships among data items or attributes can be analyzed or reported

•  Data visualization is one of the most powerful and appealing techniques for data exploration ! Humans have a well developed ability to analyze large

amounts of information that is presented visually! Can detect general patterns and trends! Can detect outliers and unusual patterns

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Barplots

•  They use horizontal or vertical bars to compare categories.

•  One axis shows the compared categories, the other axis represents a discrete value

•  Some bar graphs present bars clustered in groups of more than one (grouped bar graphs), and others show the bars divided into subparts to show cumulate effect (stacked bar graphs)

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Barplot using R

# barplot barplot(wnum$outlook) ### ### distribution of outlook values ### splitted according to attribute windy ### counts <- table(wnum$windy,wnum$outlook) barplot(counts,col=c("darkblue","red")) # horizontal barplot(counts,col=c("darkblue","red"), horiz=TRUE) # grouped barplot(counts,col=c("darkblue","red"), horiz=TRUE, beside=TRUE)

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Histograms

•  They are a graphical representation of the distribution of data !introduced by Karl Pearson in 1895

•  They estimate the probability distribution of a continuous variables

•  They are representations of tabulated frequencies depicted as adjacent rectangles, erected over discrete intervals (bins). Their areas are proportional to the frequency of the observations in the interval.

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Histograms

•  The height of each bar indicates the number of objects•  Shape of histogram depends on the number of bins

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Example: Petal Width (10 and 20 bins, respectively)


Histograms in R

# distribution of temperature values hist(wnum$temperature, xlab="Temperature",

main="Temperature Distribution", col="blue") # fewer bins hist(wnum$temperature, breaks=2, xlab="Temperature",

main="Temperature Distribution", col="blue") # fit the distribution d <- density(wnum$temperature) plot(d, main="Temperature Distribution", xlab="Temperature") polygon(d, col="red", border="blue") # difference in bins the distribution hist(iris$petalwidth, col="blue", breaks=10, xlab="Petal Width", main="") hist(iris$petalwidth, col="blue", breaks=20, xlab="Petal Width", main="") d <- density(iris$petalwidth) plot(d, main="Petal Width Distribution", xlab="Petal Width") polygon(d, col="red", border="blue")

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Maps

•  Maps are a very effective communications tool that can visualize thousands of data points in just one figure

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Mapping Data with R

# http://togaware.com/onepager/MapsO.pdf # required packages install.packages("maps") install.packages("ggmap") install.packages("oz") library(maps) library(ggmap) library(oz) library(ggplot2) library(scales) ds <- map_data("world") p <- ggplot(ds, aes(x=long, y=lat, group=group, fill=region)) p <- p + geom_polygon() p <- p + theme(legend.position = "none”)

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Mapping Data with R

# World map p <- ggplot(ds, aes(x=long, y=lat, group=group, fill=region)) p <- p + geom_polygon() p <- p + theme(legend.position = "none") p # Map of Europe map <- get_map(location="Europe", zoom=4) p <- ggmap(map) p # Google Map map <- get_map(location="Sydney", zoom=14, maptype="roadmap", source="google") p <- ggmap(map) p

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Mapping Data with R

# Mapping arrests arrests <- USArrests names(arrests) <- tolower(names(arrests)) arrests$region <- tolower(rownames(USArrests)) head(arrests) # maps the attribute state in their long/lat coordinates states <- map_data("state") # join the database of state information with the arrests information using region ds <- merge(states, arrests, sort=FALSE, by="region") # reorder the points for plotting otherwise the borders are plotted incorrectly ds <- ds[order(ds$order), ] g <- ggplot(ds, aes(long, lat, group=group, fill=ds$assault/ds$murder)) g <- g + geom_polygon() print(g)

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Mapping Data for Visualization

•  Data objects, their attributes, and the relationships among data objects are translated into graphical elements such as points, lines, shapes, and colors

•  Objects are often represented as points

•  Their attribute values can be represented as the position of the points or the characteristics of the points, e.g., color, size, and shape

•  If position is used, then the relationships of points, i.e., whether they form groups or a point is an outlier, is easily perceived.

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Data Arrangement

•  Is the placement of visual elements within a display

•  Influence on how easy it is to understand the data

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Selection

•  Is the elimination or the de-emphasis of !certain objects and attributes

•  Selection may involve choosing a subset of attributes ! Dimensionality reduction is often used to reduce the number

of dimensions to two or three! Alternatively, pairs of attributes can be considered

•  Selection may also involve choosing a subset of objects!  A region of the screen can only show so many points! Can sample, but want to preserve points in sparse areas

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Box Plots

•  Box Plots (invented by Tukey)

•  Another way of displaying the distribution of data

•  Following figure shows !the basic part of a box plot

•  IQR is the interquartile range !or Q3-Q1

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outlier

Min (> Q1 -1.5 IQR)

1st quartile (Q1)

3rd quartile (Q3)

2nd quartile (Q2)

Max ( < Q3 +1.5 IQR)


Box Plot Example 59


Boxplots in R

# set working directory setwd("~/Dropbox/Documents/Online/Corsi/DMTM/data") # load data iris = read.arff("iris.arff") boxplot(iris[,1:4], ylab="values (cm)", main="iris dataset") boxplot(iris[,1:4], ylab="values (cm)", main="iris dataset", las=2, names=c("sep len", "sep wid", "pet len", "pet wid"), col=c("lightblue","lightblue","pink","pink"), at=c(1,2,5,6)) boxplot(iris[,1:4], ylab="values (cm)", main="iris dataset", las=2, names=c("sep len", "sep wid", "pet len", "pet wid"), border=c("blue","blue","green","green"), at=c(1,2,5,6)) # more examples # http://www.r-bloggers.com/box-plot-with-r-tutorial/

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Scatter Plots

•  Attributes values determine the position

•  Two-dimensional scatter plots most common, but can have three-dimensional scatter plots

•  Often additional attributes can be displayed by using the size, shape, and color of the markers that represent the objects

•  It is useful to have arrays of scatter plots can compactly summarize the relationships of several pairs of attributes

•  Examples: http://www.statmethods.net/graphs/scatterplot.html

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Scatter Plots in R

# set working directory setwd("~/Dropbox/Documents/Online/Corsi/DMTM/data") # load data iris = read.arff("iris.arff") # attach iris to the path attach(iris) # plot scatter plot plot(petallength,sepallength, xlab="Petal Length", ylab="Sepal Length", pch=19) # linear model abline(lm(sepallength~petallength), col="red") # regression line (y~x) # local linear model lines(lowess(petallength, sepallength), col="blue") # lowess line (x,y)

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Scatter Plots in R

library(car) scatterplot(sepallength~petallength | class, data=iris, xlab="Petal Length”, ylab="Sepal Length", main="Enhanced Scatter Plot", labels=row.names(iris))

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Scatter Plot Array for Iris 64


Scatter Matrix Plots in R

# paired library(car) scatterplot(sepallength~petallength | class, data=iris, xlab="Petal Length", ylab="Sepal Length", main="Enhanced Scatter Plot", labels=row.names(iris)) png("~/Downloads/scatter1.png") # scatter plot matrix pairs(~petallength+petalwidth+sepallength+sepalwidth,data=iris, main="Simple Scatterplot Matrix") dev.off() library(car) png("~/Downloads/scatter2.png") # scatter plot matrix scatterplotMatrix(~petallength+petalwidth+sepallength+sepalwidth|class, data=iris, main="Scatter Plots vs Class") dev.off()

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Scatter Plot Combined with Box Plots 66


Scatter Plots with Box Plots

# Add boxplots to a scatterplot par(fig=c(0,0.8,0,0.8), new=TRUE) plot(mtcars$wt, mtcars$mpg, xlab="Miles Per Gallon", ylab="Car Weight") par(fig=c(0,0.8,0.55,1), new=TRUE) boxplot(mtcars$wt, horizontal=TRUE, axes=FALSE) par(fig=c(0.65,1,0,0.8),new=TRUE) boxplot(mtcars$mpg, axes=FALSE) mtext("Enhanced Scatterplot", side=3, outer=TRUE, line=-3)

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Contour Plots

•  Useful for continuous attributes measured on a spatial grid

•  They partition the plane into regions of similar values

•  The contour lines that form the boundaries of these regions connect points with equal values

•  The most common example is contour maps of elevation

•  Can also display temperature, rainfall, air pressure, etc.

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Celsius


Matrix Plots

•  Can plot the data matrix

•  This can be useful when objects are sorted according to class

•  Typically, the attributes are normalized to prevent one attribute from dominating the plot

•  Plots of similarity or distance matrices can also be useful for visualizing the relationships between objects

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Heatmaps 71

dm <- data.matrix(iris[,1:4]) heatmap(dm)


additional exampleshttp://onepager.togaware.com/PlotsO.pdf


Other Visualization Techniques

•  Star Plots ! Similar approach to parallel coordinates, !

but axes radiate from a central point! The line connecting the values of an object is a polygon

•  Chernoff Faces! Approach created by Herman Chernoff! This approach associates each attribute with a characteristic of

a face! The values of each attribute determine the appearance of the

corresponding facial characteristic! Each object becomes a separate face! Relies on human’s ability to distinguish faces

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Chernoff Faces

•  More dimensions are plotted using several features of human faces

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Prof. Pier Luca Lanzihttp://cartastrophe.files.wordpress.com/2010/06/spinelli.png


Chernoff Faces & Star/Radar Plots

# http://cran.r-project.org/web/packages/aplpack/aplpack.pdf library(foreign) library(aplpack) # set working directory setwd("~/Dropbox/Documents/Online/Corsi/DMTM/data") # load data iris = read.arff("iris.arff") # attach iris to the path attach(iris) # Chernoff faces faces(iris[1:16,1:4])

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Chernoff Faces & Star/Radar Plots

require(grDevices) stars(mtcars[, 1:7], key.loc = c(14, 2), main = "Motor Trend Cars : stars(*, full = F)", full = FALSE) # full stars stars(mtcars[, 1:7], key.loc = c(14, 1.5), main = "Motor Trend Cars : full stars()", flip.labels = FALSE) # spider radar plot stars(mtcars[, 1:7], locations = c(0, 0), radius = FALSE, key.loc = c(0, 0), main = "Motor Trend Cars", lty = 2) # adding colors palette(rainbow(12, s = 0.6, v = 0.75)) stars(mtcars[, 1:7], len = 0.8, key.loc = c(12, 1.5), main = "Motor Trend Cars", draw.segments = TRUE) # positioning stars(mtcars[, 1:7], len = 0.6, key.loc = c(1.5, 0), main = "Motor Trend Cars", draw.segments = TRUE, nrow = 6, cex = .7) dev.off() faces(mtcars[,1:7])

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examples


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dmtm 2015 - 04 data exploration

Education

pier luca lanzi http

pier luca lanzi frequency

pier luca lanzi normalization

loading data

data set

categorical data

data exploration techniques

exploratory data analysis