Know Your Data in data mining applications

DATA MINING
Lecture 3: KnowYour Data
Slides Adapted from Jiawei Han et al. and Jianlin Cheng
DEPARTMENTOFCOMPUTER
SCIENCE,UNIVERSITYOF
COLORADO,COLORADO
SPRINGS.
CS4434/5434ANDDASE4435
DATAMINING,
FALL2023
DR.OLUWATOSIN
OLUWADARE,2023

2
Data Mining:
Concepts and Techniques
— Chapter 2 —
Jiawei Han, Micheline Kamber, and Jian Pei
University of Illinois at Urbana-Champaign
Simon Fraser University
©2011 Han, Kamber, and Pei. All rights reserved.

3
Chapter 2: Getting to Know Your Data
 Data Objects and Attribute Types
 Basic Statistical Descriptions of Data
 Data Visualization
 Measuring Data Similarity and Dissimilarity
 Summary

4
Types of Data Sets
 Record
 Relational records
 Data matrix, e.g., numerical matrix,
crosstabs
 Document data: text documents: term-
frequency vector
 Transaction data
 Graph and network
 World Wide Web
 Social or information networks
 Molecular Structures
 Ordered
 Video data: sequence of images
 Temporal data: time-series
 Sequential Data: transaction sequences
 Genetic sequence data
 Spatial, image and multimedia:
 Spatial data: maps
 Image data:
 Video data:
Document 1
season
timeout
lost
wi
n
game
score
ball
pla
y
coach
team
Document 2
Document 3
3 0 5 0 2 6 0 2 0 2
0
0
7 0 2 1 0 0 3 0 0
1 0 0 1 2 2 0 3 0
TID Items
1 Bread, Coke, Milk
2 Beer, Bread
3 Beer, Coke, Diaper, Milk
4 Beer, Bread, Diaper, Milk
5 Coke, Diaper, Milk

5
Important Characteristics of Structured
Data
 Dimensionality
 Curse of dimensionality
 Sparsity
 Only presence counts
 Resolution
 Patterns depend on the scale
 Distribution
 Centrality and dispersion

6
Data Objects
 Data sets are made up of data objects.
 A data object represents an entity.
 Examples:
 sales database: customers, store items, sales
 medical database: patients, treatments
 university database: students, professors, courses
 Also called samples , examples, instances, data points,
objects, tuples.
 Data objects are described by attributes.
 Database rows -> data objects; columns ->attributes.

7
Attributes
 Attribute (or dimensions, features, variables):
a data field, representing a characteristic or feature
of a data object.
 E.g., customer _ID, name, address
 Types:
 Nominal
 Binary
 Numeric: quantitative
 Interval-scaled
 Ratio-scaled

Data Attributes
 Attribute refers to the characteristic of the data
object.
 The nouns defining the characteristics are used
interchangeably: Attribute, dimension, feature,
and variable.
8
Field
Data Warehousing
Database and Data Mining
Statistic
Machine Learning
Characteristic term Used
Feature
Attribute
Variable
Dimension

9
Attribute Types
 Nominal: categories, states, or “names of things”
 Hair_color = {auburn, black, blond, brown, grey, red, white}
 marital status, occupation, ID numbers, zip codes
 Binary
 Nominal attribute with only 2 states (0 and 1)
 Symmetric binary: both outcomes equally important
 e.g., cat or dog
 Asymmetric binary: outcomes not equally important.
 e.g., medical test (positive vs. negative)
 Convention: assign 1 to most important outcome (e.g., HIV
positive)
 the positive (1) and negative (0) outcomes of a disease test.
 Ordinal
 Values have a meaningful order (ranking) but magnitude between
successive values is not known.
 Size = {small, medium, large}, grades, army rankings

10
Numeric Attribute Types
 Quantity (integer or real-valued)
 Interval
 Measured on a scale of equal-sized units
 Values have order
 E.g., temperature in C˚or F˚, calendar dates
 No true zero-point
 Ratio
 Inherent zero-point
 We can speak of values as being an order of
magnitude larger than the unit of measurement
(10 K˚ is twice as high as 5 K˚).
 e.g., temperature in Kelvin, length, counts,
monetary quantities

11
Discrete vs. Continuous Attributes
 Discrete Attribute
 Has only a finite or countably infinite set of values
 E.g., zip codes, profession, or the set of words in a
collection of documents
 Sometimes, represented as integer variables
 Note: Binary attributes are a special case of discrete
attributes
 Continuous Attribute
 Has real numbers as attribute values
 E.g., temperature, height, or weight
 Practically, real values can only be measured and
represented using a finite number of digits
 Continuous attributes are typically represented as
floating-point variables

12
 Summary

13
Basic Statistical Descriptions of Data
 Motivation
 To better understand the data: central tendency,
variation and spread
 Data dispersion characteristics
 median, max, min, quantiles, outliers, variance, etc.
 Numerical dimensions correspond to sorted intervals
 Data dispersion: analyzed with multiple granularities
of precision
 Boxplot or quantile analysis on sorted intervals
 Dispersion analysis on computed measures
 Folding measures into numerical dimensions
 Boxplot or quantile analysis on the transformed cube

14
Measuring the Central Tendency
 Mean (algebraic measure) (sample vs. population):
Note: n is sample size and N is population size.
 Weighted arithmetic mean:
 Trimmed mean: chopping extreme values
 Median:
 Middle value if odd number of values, or average of
the middle two values otherwise
 Estimated by interpolation (for grouped data):
 Mode
 Value that occurs most frequently in the data
 Unimodal, bimodal, trimodal
 Empirical formula:
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May 8, 2024 Data Mining: Concepts and Techniques 15
Symmetric vs. Skewed
Data
 Median, mean and mode of
symmetric, positively and
negatively skewed data
positively skewed negatively skewed
symmetric

16
Measuring the Dispersion of Data
 Quartiles, outliers and boxplots
 Quartiles: Q1 (25th percentile), Q3 (75th percentile)
 Inter-quartile range: IQR = Q3 – Q1
 Five number summary: min, Q1, median, Q3, max
 Boxplot: ends of the box are the quartiles; median is marked; add
whiskers, and plot outliers individually
 Outlier: usually, a value higher/lower than Q3 + 1.5 x IQR or Q1 – 1.5 x
IQR
 Variance and standard deviation (sample: s, population: σ)
 Variance: (algebraic, scalable computation)
 Standard deviation s (or σ) is the square root of variance s2 (or σ2)
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17
Boxplot Analysis
 Five-number summary of a distribution
 Minimum, Q1, Median, Q3, Maximum
 Boxplot
 Data is represented with a box
 The ends of the box are at the first and third
quartiles, i.e., the height of the box is IQR
 The median is marked by a line within the
box
 Whiskers: two lines outside the box extended
to Minimum and Maximum
 Outliers: points beyond a specified outlier
threshold, plotted individually

Boxplot Analysis Example
 Distribution A is positively skewed, because the whisker and half-box are longer on
the right side of the median than on the left side.
 Distribution B is approximately symmetric, because both half-boxes are almost the
same length (0.11 on the left side and 0.10 on the right side).
 Distribution C is negatively skewed because the whisker and half-box are longer on
the left side of the median than on the right side.
18
https://www150.statcan.gc.ca/n1/edu/power-pouvoir/ch12/5214889-eng.htm

May 8, 2024 Data Mining: Concepts and Techniques 19
Visualization of Data Dispersion: 3-D Boxplots

20
Properties of Normal Distribution Curve
 The normal (distribution) curve
 From μ–σ to μ+σ: contains about 68% of the
measurements (μ: mean, σ: standard deviation)
 From μ–2σ to μ+2σ: contains about 95% of it
 From μ–3σ to μ+3σ: contains about 99.7% of it

Standard deviation in a Normal Distribution
21
Images/google

22
Graphic Displays of Basic Statistical
Descriptions
 Boxplot: graphic display of five-number summary
 Histogram: x-axis are values, y-axis repres. frequencies
 Quantile plot: each value xi is paired with fi indicating
that approximately 100 fi % of data are  xi
 Quantile-quantile (q-q) plot: graphs the quantiles of
one univariant distribution against the corresponding
quantiles of another
 Scatter plot: each pair of values is a pair of coordinates
and plotted as points in the plane

23
Histogram Analysis
 Histogram: Graph display of
tabulated frequencies, shown as
bars
 It shows what proportion of cases
fall into each of several categories
 Differs from a bar chart in that it is
the area of the bar that denotes the
value, not the height as in bar
charts, a crucial distinction when the
categories are not of uniform width
 The categories are usually specified
as non-overlapping intervals of
some variable. The categories (bars)
must be adjacent
0
5
10
15
20
25
30
35
40
10000 30000 50000 70000 90000

Homework 1
 Homework 1 has been posted at the course web
site and on Canvas.
 Due Sept. 12, 2023
 Submit it to Canvas
May 8, 2024
Data Mining: Concepts and Techniques 24

25
Histograms Often Tell More than Boxplots
 The two histograms
shown in the left may
have the same boxplot
representation
 The same values
for: min, Q1,
median, Q3, max
 But they have rather
different data
distributions

Data Mining: Concepts and Techniques 26
Quantile Plot
 Displays all of the data (allowing the user to assess both
the overall behavior and unusual occurrences)
 Plots quantile information
 For a data xi data sorted in increasing order, fi
indicates that approximately 100 fi% of the data are
below or equal to the value xi

27
Quantile-Quantile (Q-Q) Plot
 Graphs the quantiles of one univariate distribution against the
corresponding quantiles of another
 View: Is there is a shift in going from one distribution to another?
 Example shows unit price of items sold at Branch 1 vs. Branch 2 for
each quantile. Unit prices of items sold at Branch 1 tend to be lower
than those at Branch 2.

28
Scatter plot
 Provides a first look at bivariate data to see clusters of
points, outliers, etc
 Each pair of values is treated as a pair of coordinates and
plotted as points in the plane

29
Positively and Negatively Correlated Data
 The left half fragment is positively
correlated
 The right half is negative correlated

31
 Summary

32
Similarity and Dissimilarity
 Similarity
 Numerical measure of how alike two data objects are
 Value is higher when objects are more alike
 Often falls in the range [0,1]
 Dissimilarity (e.g., distance)
 Numerical measure of how different two data objects
are
 Lower when objects are more alike
 Minimum dissimilarity is often 0
 Upper limit varies
 Proximity refers to a similarity or dissimilarity

33
Data Matrix and Dissimilarity Matrix
 Data matrix
 n data points with p
dimensions
 Two modes
 Dissimilarity matrix
 n data points, but
registers only the
distance
 A triangular matrix
 Single mode
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34
Proximity Measure for Nominal Attributes
 Can take 2 or more states, e.g., red, yellow, blue,
green (generalization of a binary attribute)
 Method 1: Simple matching
 m: # of matches, p: total # of variables
 Method 2: Use a large number of binary attributes
 creating a new binary attribute for each of the
M nominal states
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Class Example: Method 1
35
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36
Proximity Measure for Binary Attributes
 A contingency table for binary data
 Distance measure for symmetric
binary variables:
 Distance measure for asymmetric
binary variables:
 Jaccard coefficient (similarity
measure for asymmetric binary
variables):
 Note: Jaccard coefficient is the same as “coherence”:
Object i
Object j

Variables (q, r, s ,t)
 q is the number of attributes that equal 1 for
both objects i and j,
 r is the number of attributes that equal 1 for
object i but equal 0 for object j,
 s is the number of attributes that equal 0 for
object i but equal 1 for object j, and
 t is the number of attributes that equal 0 for both
objects i and j.
37

38
Dissimilarity between Binary Variables
 Example
 Gender is a symmetric attribute
 The remaining attributes are asymmetric binary attributes
 Let the values Y(yes) and P(positive) be 1, and the value N(no
and negative) 0
Name Gender Fever Cough Test-1 Test-2 Test-3 Test-4
Jack M Y N P N N N
Mary F Y N P N P N
Jim M Y P N N N N

Calculate the Dissimilarity
 d(Jack, Mary) = ?
 d(Jack, Jim). = ?
 d(Jim, Jack) = ?
 q is the number of attributes that equal 1 for both objects i and j,
 r is the number of attributes that equal 1 for object i but equal 0 for object j,
 s is the number of attributes that equal 0 for object i but equal 1 for object j,
and
 t is the number of attributes that equal 0 for both objects i and j.
39
OR

40
Dissimilarity between Binary Variables
 Example
 Gender is a symmetric attribute
 The remaining attributes are asymmetric binary attributes
 Let the values Y(yes) and P(positive) be 1, and the value N(no
and negative) 0
Name Gender Fever Cough Test-1 Test-2 Test-3 Test-4
Jack M Y N P N N N
Mary F Y N P N P N
Jim M Y P N N N N
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Comment on the Result
 What does the measurement suggest?
 These measurements suggest that Jim and
Mary are unlikely to have a similar disease
because they have the highest dissimilarity
value among the three pairs.
 Of the three patients, Jack and Mary are the
most likely to have a similar disease.
41

42
Standardizing Numeric Data
 Z-score:
 X: raw score to be standardized, μ: mean of the population, σ:
standard deviation
 the distance between the raw score and the population mean in
units of the standard deviation
 negative when the raw score is below the mean, “+” when above
 An alternative way: Calculate the mean absolute deviation
where
 standardized measure (z-score):
 Using mean absolute deviation is more robust than using standard
deviation
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43
Example:
Data Matrix and Dissimilarity Matrix
point attribute1 attribute2
x1 1 2
x2 3 5
x3 2 0
x4 4 5
Dissimilarity Matrix
(with Euclidean Distance)
x1 x2 x3 x4
x1 0
x2 3.61 0
x3 5.1 5.1 0
x4 4.24 1 5.39 0
Data Matrix

44
Distance on Numeric Data: Minkowski
Distance
 Minkowski distance: A popular distance measure
where i = (xi1, xi2, …, xip) and j = (xj1, xj2, …, xjp) are two
p-dimensional data objects, and h is the order (the
distance so defined is also called L-h norm)
 Properties
 d(i, j) > 0 if i ≠ j, and d(i, i) = 0 (Positive definiteness)
 d(i, j) = d(j, i) (Symmetry)
 d(i, j)  d(i, k) + d(k, j) (Triangle Inequality)
 A distance that satisfies these properties is a metric

45
Special Cases of Minkowski Distance
 h = 1: Manhattan (city block, L1 norm) distance
 E.g., the Hamming distance: the number of bits that are
different between two binary vectors
 h = 2: (L2 norm) Euclidean distance
 h  . “supremum” (Lmax norm, L norm) distance.
 This is the maximum difference between any component
(attribute) of the vectors
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46
Example: Minkowski Distance
Dissimilarity Matrices
point attribute 1 attribute 2
x1 1 2
x2 3 5
x3 2 0
x4 4 5
L x1 x2 x3 x4
x1 0
x2 5 0
x3 3 6 0
x4 6 1 7 0
L2 x1 x2 x3 x4
x1 0
x2 3.61 0
x3 2.24 5.1 0
x4 4.24 1 5.39 0
L x1 x2 x3 x4
x1 0
x2 3 0
x3 2 5 0
x4 3 1 5 0
Manhattan (L1)
Euclidean (L2)
Supremum

47
Ordinal Variables
 An ordinal variable can be discrete or continuous
 Order is important, e.g., rank
 Can be treated like interval-scaled
 replace xif by their rank
 map the range of each variable onto [0, 1] by replacing
i-th object in the f-th variable by
 compute the dissimilarity using methods for interval-
scaled variables
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48
Attributes of Mixed Type
 A database may contain all attribute types
 Nominal, symmetric binary, asymmetric binary, numeric,
ordinal
 One may use a weighted formula to combine their effects
 f is binary or nominal:
dij
(f) = 0 if xif = xjf , or dij
(f) = 1 otherwise
 f is numeric: use the normalized distance
 f is ordinal
 Compute ranks rif and
 Treat zif as interval-scaled
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49
Cosine Similarity
 A document can be represented by thousands of attributes, each
recording the frequency of a particular word (such as keywords) or
phrase in the document.
 Other vector objects: gene features in micro-arrays, …
 Applications: information retrieval, biologic taxonomy, gene feature
mapping, ...
 Cosine measure: If d1 and d2 are two vectors (e.g., term-frequency
vectors), then
cos(d1, d2) = (d1  d2) /||d1|| ||d2|| ,
where  indicates vector dot product, ||d||: the length of vector d

50
Example: Cosine Similarity
 cos(d1, d2) = (d1  d2) /||d1|| ||d2|| ,
where  indicates vector dot product, ||d|: the length of vector d
 Ex: Find the similarity between documents 1 and 2.
d1 = (5, 0, 3, 0, 2, 0, 0, 2, 0, 0)
d2 = (3, 0, 2, 0, 1, 1, 0, 1, 0, 1)
d1d2 = 5*3+0*0+3*2+0*0+2*1+0*1+0*1+2*1+0*0+0*1 = 25
||d1||= (5*5+0*0+3*3+0*0+2*2+0*0+0*0+2*2+0*0+0*0)0.5=(42)0.5
= 6.481
||d2||= (3*3+0*0+2*2+0*0+1*1+1*1+0*0+1*1+0*0+1*1)0.5=(17)0.5
= 4.12
cos(d1, d2 ) = 0.94

51
 Summary

Summary
 Data attribute types: nominal, binary, ordinal, interval-scaled, ratio-
scaled
 Many types of data sets, e.g., numerical, text, graph, Web, image.
 Gain insight into the data by:
 Basic statistical data description: central tendency, dispersion,
graphical displays
 Data visualization: map data onto graphical primitives
 Measure data similarity
 Above steps are the beginning of data preprocessing.
 Many methods have been developed but still an active area of research.
52

References
 W. Cleveland, Visualizing Data, Hobart Press, 1993
 T. Dasu and T. Johnson. Exploratory Data Mining and Data Cleaning. John Wiley, 2003
 U. Fayyad, G. Grinstein, and A. Wierse. Information Visualization in Data Mining and
Knowledge Discovery, Morgan Kaufmann, 2001
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