DMTM 2015 - 04 Data Exploration

Prof. Pier Luca Lanzi
Data Exploration!
Data Mining andText 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/
2

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
4

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!
5

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
7

numerical attributes

Geometric Interpretation of Correlation
•  The correlation coefﬁcient is simply the cosine of the angle
between the two centered attribute vectors
20

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
37

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
38

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
39

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
40

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%
41

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))
42

# 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")])
43

# 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))
44

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
45

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)
46

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)
47

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.
48

Histograms
•  The height of each bar indicates the number of objects
•  Shape of histogram depends on the number of bins
49
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")
50

Maps
•  Maps are a very effective communications tool that can visualize
thousands of data points in just one ﬁgure
51

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”)
52

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
53

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)
54

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.
55

Data Arrangement
•  Is the placement of visual elements within a display
•  Inﬂuence on how easy it is to understand the data
56

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
57

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
58
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
# 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/
60

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
61

Scatter Plots in R
# load data
# 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)
62

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))
63

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()
65

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)
67

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.
68

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
70

Heatmaps 71
dm <- data.matrix(iris[,1:4])
heatmap(dm)

additional examples
http://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
73

Chernoff Faces
•  More dimensions are plotted using several features of human faces
76

http://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)
# load data
# attach iris to the path
attach(iris)
# Chernoff faces
faces(iris[1:16,1:4])
79

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])
80

examples

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“Here’s the skinny, 66% of attention on a normal media page is spent
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scroll right past that and spend their time where the content not the
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http://time.com/12933/what-you-think-you-know-about-the-web-is-wrong/?iid=biz-category-mostpop2

http://apps.startribune.com/news/20140313-beer-me-minnesota/

DMTM 2015 - 04 Data Exploration

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