[系列活動] 資料探勘速遊

Quick Tour of Data Mining

Yi-Shin Chen

Institute of Information Systems and Applications

Department of Computer Science

National Tsing Hua University

[email protected]

About Speaker

陳宜欣 Yi-Shin Chen

▷Currently• 清華大學資訊工程系副教授• 主持智慧型資料工程與應用實驗室 (IDEA Lab)

▷Education• Ph.D. in Computer Science, USC, USA

• M.B.A. in Information Management, NCU, TW

• B.B.A. in Information Management, NCU, TW

▷Courses (all in English)

• Research and Presentation Skills

• Introduction to Database Systems

• Advanced Database Systems

• Data Mining: Concepts, Techniques, and

Applications

2

Evolution of Data

Management

The relationships between the techniques and our world

3

4

1900 1920 1940 1950 1960 1970

Manual

Record

Managers

1950: Univac had developed

a magnetic tape

1951: Univac I delivered to

the US Census Bureau

1931: Gödel's Incompleteness

Theorem 1948: Information theory (by

Shannon)

Information Entropy

1944: Mark I(Server) 1963: The origins of the Internet

Programmed Record

Managers• Birth of high-level

programming

languages

• Batch processingPunched-Card

Record Managers

On-line Network

Databases• Indexed sequential

records

• Data independence

• Concurrent Access

2001: Data Science

2009: Deep Learning

5

1970 1980 1990 2000 2010

1985: 1st standardized

of SQL

1976: E-R Model by

Peter Chen1993: WWW

2006: Amazon.com Elastic

Compute Cloud

1980: Artificial Neural

Networks

Knowledge Discovery

in Databases

Object Relational

Model• Support multiple

datatypes and

applications

1974: IBM System R

Relational Model• Give Database users

high-level set-oriented

data access

operations

Data Mining

What we know, and what we do now

6

Data Mining

▷What is data mining?

• Algorithms for seeking unexpected “pearls of wisdom”

▷Current data mining research:

• Focus on efficient ways to discover models of existing data sets

• Developed algorithms are: classification, clustering, association-

rule discovery, summarization…etc.

7

Data Mining Examples

8Slide from: Prof. Shou-De Lin

Origins of Data Mining

▷Draws ideas from

• Machine learning/AI

• Pattern recognition

• Statistics

• Database systems

▷ Traditional Techniques may be unsuitable due to

• Enormity of data

• High dimensionality of data

• Heterogeneous, distributed nature of data

9© Tan, Steinbach, Kumar Introduction to Data Mining

Data Mining

Machine Learning/AI

Pattern Recognition Statistics

Database

Knowledge Discovery (KDD) Process

10

Data CleaningData Integration

Databases

Data

Warehouse

Task-relevant

Data

Selection

Data Mining

Pattern

Evaluation

Database

11

Database

12

Database

13

Informal Design Guidelines for Database

▷Design a schema that can be explained easily relation by

relation. The semantics of attributes should be easy to interpret

▷Should avoid update anomaly problems

▷Relations should be designed such that their tuples will have as

few NULL values as possible

▷ The relations should be designed to satisfy the lossless join

condition (guarantee meaningful results for join operations)

14

Data Warehouse

▷Assemble and manage data from various sources

for the purpose of answering business questions

15

CRM ERP POS …OLTP

Data Warehouse

Meaningful

Knowledge Discovery (KDD) Process

16

Data CleaningData Integration

Databases

Data

Warehouse

Task-relevant

Data

Selection

Data Mining

Pattern

Evaluation

KDD Process: Several Key Steps

▷Pre-processing

• Learning the application domain

→ Relevant prior knowledge and goals of application

• Creating a target data set: data selection

• Data cleaning and preprocessing: (may take 60% of effort!)

• Data reduction and transformation

→ Find useful features

▷Data mining

• Choosing functions of data mining

→ Choosing the mining algorithm

• Search for patterns of interest

▷Evaluation

• Pattern evaluation and knowledge presentation

→ visualization, transformation, removing redundant patterns, etc.17

© Han & Kamper Data Mining: Concepts and Techniques

Data

Many slides provided by Tan, Steinbach, Kumar for book “Introduction to Data Mining” are adapted in this presentation

The most important part in the whole process

18

Types of Attributes

▷There are different types of attributes

• Nominal (=,≠)

→ Nominal values can only distinguish one object from

another

→ Examples: ID numbers, eye color, zip codes

• Ordinal (<,>)

→ Ordinal values can help to order objects

→ Examples: rankings, grades

• Interval (+,-)

→ The difference between values are meaningful

→ Examples: calendar dates

• Ratio (*,/)

→ Both differences and ratios are meaningful

→ Examples: temperature in Kelvin, length, time, counts

19只有這一種能適用所有的處理方法

Types of Data Sets

▷Record

• Data Matrix

• Document Data

• Transaction Data

▷Graph

• World Wide Web

• Molecular Structures

▷Ordered

• Spatial Data

• Temporal Data

• Sequential Data

• Genetic Sequence Data

20

1.12.216.226.2512.65

1.22.715.225.2710.23

Thickness LoadDistanceProjection

of y load

Projection

of x Load

1.12.216.226.2512.65

1.22.715.225.2710.23

Thickness LoadDistanceProjection

of y load

Projection

of x Load

Document 1

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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 Time Items

1 2009/2/8 Bread, Coke, Milk

2 2009/2/13 Beer, Bread

3 2009/2/23 Beer, Diaper

4 2009/3/1 Coke, Diaper, Milk

A Facebook Example

21

Data Matrix/Graph Data Example

22

Document Data

23

Transaction Data

24

Spatio-Temporal Data

25

Sequential Data

26

2017/1/3

2016/12/31

2016/12/31

2016/11/28

2016/11/17

2016/11/09

2016/11/08

2016/11/08

2016/11/08

2016/11/08

2016/11/05

Tips for Converting Text to

Numerical Values

27

Recap: Types of Attributes

▷There are different types of attributes

• Nominal (=,≠)

→ Nominal values can only distinguish one object from

another

→ Examples: ID numbers, eye color, zip codes

• Ordinal (<,>)

→ Ordinal values can help to order objects

→ Examples: rankings, grades

• Interval (+,-)

→ The difference between values are meaningful

→ Examples: calendar dates

• Ratio (*,/)

→ Both differences and ratios are meaningful

→ Examples: temperature in Kelvin, length, time, counts

28

Vector Space Model

▷Represent the keywords of objects using a term vector

• Term: basic concept, e.g., keywords to describe an object

• Each term represents one dimension in a vector

• N total terms define an n-element terms

• Values of each term in a vector corresponds to the

importance of that term

▷Measure similarity by the vector distances

29

Document 1

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tea

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Document 2

Document 3

3 0 5 0 2 6 0 2 0 2

0

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7 0 2 1 0 0 3 0 0

1 0 0 1 2 2 0 3 0

Term Frequency and Inverse

Document Frequency (TFIDF)

▷Since not all objects in the vector space are equally

important, we can weight each term using its

occurrence probability in the object description

• Term frequency: TF(d,t)

→ number of times t occurs in the object description d

• Inverse document frequency: IDF(t)

→ to scale down the terms that occur in many descriptions

30

Normalizing Term Frequency

▷nij represents the number of times a term ti occurs in

a description dj . tfij can be normalized using the total

number of terms in the document

• 𝑡𝑓𝑖𝑗 =𝑛𝑖𝑗

𝑁𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑𝑉𝑎𝑙𝑢𝑒

▷NormalizedValue could be:• Sum of all frequencies of terms

• Max frequency value

• Any other values can make tfij between 0 to 1

31

Inverse Document Frequency

▷ IDF seeks to scale down the coordinates of terms

that occur in many object descriptions

• For example, some stop words(the, a, of, to, and…) may

occur many times in a description. However, they should

be considered as non-important in many cases

• 𝑖𝑑𝑓𝑖 = 𝑙𝑜𝑔𝑁

𝑑𝑓𝑖+ 1

→ where dfi (document frequency of term ti) is the

number of descriptions in which ti occurs

▷ IDF can be replaced with ICF (inverse class frequency) and

many other concepts based on applications

32

Reasons of Log

▷ Each distribution can indicate the hidden force•

•

•

33

Power-law distribution Normal distribution Normal distribution

Data Quality

Dirty Data

34

Big Data?

▷ “Every day, we create 2.5 quintillion bytes of data — so much

that 90% of the data in the world today has been created in the

last two years alone. This data comes from everywhere:

sensors used to gather climate information, posts to social

media sites, digital pictures and videos, purchase transaction

records, and cell phone GPS signals to name a few. This data

is “big data.”

• --from www.ibm.com/software/data/bigdata/what-is-big-data.html

35

http://www.ibm.com/software/data/bigdata/what-is-big-data.html

4V

36

Data Quality

▷What kinds of data quality problems?

▷How can we detect problems with the data?

▷What can we do about these problems?

▷Examples of data quality problems:

•Noise and outliers

•Missing values

•Duplicate data

37

Noise

▷Noise refers to modification of original values

• Examples: distortion of a person’s voice when talking

on a poor phone and “snow” on television screen

38Two Sine Waves Two Sine Waves + Noise

Outliers

▷Outliers are data objects with characteristics

that are considerably different than most of

the other data objects in the data set

39

Missing Values

▷Reasons for missing values

• Information is not collected

→ e.g., people decline to give their age and weight

• Attributes may not be applicable to all cases

→ e.g., annual income is not applicable to children

▷Handling missing values

• Eliminate Data Objects

• Estimate Missing Values

• Ignore the Missing Value During Analysis

• Replace with all possible values

→ Weighted by their probabilities

40

Duplicate Data

▷Data set may include data objects that are

duplicates, or almost duplicates of one another• Major issue when merging data from heterogeneous sources

▷Examples:• Same person with multiple email addresses

▷Data cleaning• Process of dealing with duplicate data issues

41

Data Preprocessing

To be or not to be

42

Data Preprocessing

▷Aggregation

▷Sampling

▷Dimensionality reduction

▷Feature subset selection

▷Feature creation

▷Discretization and binarization

▷Attribute transformation

43

Aggregation

▷Combining two or more attributes (or objects) into a single

attribute (or object)

▷Purpose• Data reduction

→ Reduce the number of attributes or objects

• Change of scale

→ Cities aggregated into regions, states, countries, etc

• More “stable” data

→ Aggregated data tends to have less variability

44

SELECT d.Name, avg(Salary)

FROM Employee AS e, Department AS d

WHERE e.Dept=d.DNo

GROUP BY d.Name

HAVING COUNT(e.ID)>=2;

Sampling

▷Sampling is the main technique employed for data

selection

• It is often used for both

→ Preliminary investigation of the data

→ The final data analysis

• Reasons:

→ Statistics: Obtaining the entire set of data of interest is too

expensive

→ Data mining: Processing the entire data set is too

expensive

45

Key Principle For Effective Sampling

▷The sample is representative

•Using a sample will work almost as well as using

the entire data sets

•The approximately the same property as the

original set of data

46

Sample Size Matters

47

8000 points 2000 Points 500 Points

Sampling Bias

▷ 2004 Taiwan presidential election polls

48

TVBS

聯合報

訪問日期 93 年 1 月 15日至 1 月 17日有效樣本 1068 人拒訪 699 人抽樣誤差在 95% 信心水準下，約 ± 3個百分點訪問地區台灣地區抽樣方法電話簿分層系統抽樣，電話號碼末二位隨機

Dimensionality Reduction

▷Purpose:• Avoid curse of dimensionality• Reduce amount of time and memory required by data

mining algorithms• Allow data to be more easily visualized• May help to eliminate irrelevant features or reduce noise

▷Techniques• Principle Component Analysis• Singular Value Decomposition• Others: supervised and non-linear techniques

49

Curse of Dimensionality

▷When dimensionality increases, data becomes

increasingly sparse in the space that it occupies

• Definitions of density and distance between points, which is

critical for clustering and outlier detection, become less

meaningful

50

• Randomly generate 500

points

• Compute difference

between max and min

distance between any pair

of points

Dimensionality Reduction: PCA

▷Goal is to find a projection that captures

the largest amount of variation in data

51

x2

x1

e

Feature Subset Selection

▷Another way to reduce dimensionality of data

▷Redundant features

•Duplicate much or all of the information contained in

one or more other attributes

•E.g. purchase price of a product vs. sales tax

▷Irrelevant features

•Contain no information that is useful for the data

mining task at hand

•E.g. students' ID is often irrelevant to the task of

predicting students' GPA

52

Feature Creation

▷Create new attributes that can capture the

important information in a data set much

more efficiently than the original attributes

▷Three general methodologies:

•Feature extraction

→Domain-specific

•Mapping data to new space

•Feature construction

→Combining features

53

Mapping Data to a New Space

▷Fourier transform

▷Wavelet transform

54

Two Sine

WavesTwo Sine Waves +

NoiseFrequency

Discretization Using Class Labels

▷Entropy based approach

55

3 categories for both x and y 5 categories for both x and y

Discretization Without Using Class Labels

56

Attribute Transformation

▷A function that maps the entire set of values of a

given attribute to a new set of replacement values

• So each old value can be identified with one of the new

values

• Simple functions: xk, log(x), ex, |x|

• Standardization and Normalization

57

Transformation Examples

58

Log (

Fre

quency)

Log(L

og (

Fre

quency))

Preprocessing in Reality

59

Data Collection

▷Align /Classify the attributes correctly

60

Who post this message Mentioned User

HashtagShared URL

Language Detection

▷To detect an language (possible languages)

in which the specified text is written

▷Difficulties

•Short message

•Different languages in one statement

•Noisy61

你好現在幾點鐘apa kabar sekarang jam berapa ?

繁體中文 (zh-tw)印尼文 (id)

Wrong Detection Examples

▷Twitter examples

62

@sayidatynet top song #LailaGhofran

shokran ya garh new album #listen

中華隊的服裝挺特別的，好藍。。。#ChineseTaipei #Sochi #2014冬奧

授業前の雪合戦w http://t.co/d9b5peaq7J

Before / after removing noise

en -> id

it -> zh-tw

en -> ja

Removing Noise

▷Removing noise before detection•Html file ->tags

•Twitter -> hashtag, mention, URL

63

<meta name=\"twitter:description\"content=\"觸犯法國隱私法〔駐歐洲特派記者胡蕙寧、國際新聞中心／綜合報導〕網路搜尋引擎巨擘 Google8 日在法文版首頁（www.google.fr）張貼悔過書 ...\"/>

觸犯法國隱私法〔駐歐洲特派記者胡蕙寧、國際新聞中心／綜合報導〕網路搜尋引擎巨擘Google8日在法文版首頁（www.google.fr）張貼悔過書 ...

英文(en)

繁中(zh-tw)

Data Cleaning

▷Special character

▷Utilize regular expressions to clean data

64

Unicode emotions ☺, ♥…

Symbol icon ☏, ✉…

Currency symbol €, £, $...

Tweet URL

Filter out non-(letters, space,

punctuation, digit) ◕‿◕ Friendship is everything ♥ ✉

[email protected]

I added a video to a @YouTube playlist

http://t.co/ceYX62StGO Jamie Riepe(^|\\s*)http(\\S+)?(\\s*|$)

(\\p{L}+)|(\\p{Z}+)|

(\\p{Punct}+)|(\\p{Digit}+)

Japanese Examples

▷Use regular expression remove all

special words

•うふふふふ(*^^*)楽しむ！ありがとうございま

す^o^ アイコン、ラブラブ(-_-)♡

•うふふふふ楽しむありがとうございますア

イコンラブラブ

65

\\W

Part-of-speech (POS) Tagging

▷Processing text and assigning parts of

speech to each word

▷Twitter POS tagging

•Noun (N), Adjective (A), Verb (V), URL (U)…

66

Happy Easter! I went to work and came home to an empty house now im

going for a quick run http://t.co/Ynp0uFp6oZ

Happy_A Easter_N !_, I_O went_V to_P work_N and_& came_V home_N

to_P an_D empty_A house_N now_R im_L going_V for_P a_D quick_A

run_N http://t.co/Ynp0uFp6oZ_U

Stemming

▷@DirtyDTran gotta be caught up for

tomorrow nights episode

▷@ASVP_Jaykey for some reasons I found

this very amusing

67

• @DirtyDTran gotta be catch up for tomorrow night episode

• @ASVP_Jaykey for some reason I find this very amusing

RT @kt_biv : @caycelynnn loving and missing you! we are

still looking for Lucy

love miss be

look

Hashtag Segmentation

▷By using Microsoft Web N-Gram Service

(or by using Viterbi algorithm)

68

#pray #for #boston

Wow! explosion at a boston race ... #prayforboston

#citizenscience

#bostonmarathon

#goodthingsarecoming

#lowbloodpressure

→

→

→

→

#citizen #science

#boston #marathon

#good #things #are #coming

#low #blood #pressure

More Preprocesses for Different Web

Data

▷Extract source code without javascript

▷Removing html tags

69

Extract Source Code Without Javascript

▷Javascript code should be considered as an exception

• it may contain hidden content

70

Remove Html Tags

▷Removing html tags to extract meaningful content

71

More Preprocesses for Different Languages

▷Chinese Simplified/Traditional Conversion

▷Word segmentation

72

Chinese Simplified/Traditional Conversion

▷Word conversion• 请乘客从后门落车 → 請乘客從後門下車

▷One-to-many mapping• @shinrei 出去旅游还是崩坏 → @shinrei 出去旅游還是崩壞

游 (zh-cn) → 游|遊 (zh-tw)

▷Wrong segmentation• 人体内存在很多微生物 → 內存: 人體記憶體在很多微生物

→ 存在: 人體內存在很多微生物

73

內存|存在

Wrong Chinese Word Segmentation

▷Wrong segmentation• 這(Nep) 地面(Nc) 積(VJ) 還(D) 真(D) 不(D) 小(VH) http://t.co/QlUbiaz2Iz

▷Wrong word• @iamzeke 實驗(Na) 室友(Na) 多(Dfa) 危險(VH) 你(Nh) 不(D) 知道(VK) 嗎

(T) ?

▷Wrong order

• 人體(Na) 存(VC) 內在(Na) 很多(Neqa) 微生物(Na)

▷Unknown word

• 半夜(Nd) 逛團(Na) 購(VC) 看到(VE) 太(Dfa) 吸引人(VH) !!

74

地面|面積

實驗室|室友

存在|內在

未知詞:團購

Similarity and Dissimilarity

To like or not to like

75

Similarity and Dissimilarity

▷Similarity

• Numerical measure of how alike two data objects are.

• Is higher when objects are more alike.

• Often falls in the range [0,1]

▷Dissimilarity

• Numerical measure of how different are two data objects

• Lower when objects are more alike

• Minimum dissimilarity is often 0

• Upper limit varies

76

Euclidean Distance

Where n is the number of dimensions (attributes) and pk and qk are, respectively, the kth attributes (components) or data objects p and q.

▷Standardization is necessary, if scales differ.

77

n

kkk qpdist

1

2)(

Minkowski Distance

▷Minkowski Distance is a generalization of Euclidean Distance

Where r is a parameter, n is the number of dimensions (attributes) and pk and qk are, respectively, the kth attributes (components) or data objects p and q.

78

rn

k

rkk qpdist

1

1)||(

: is extremely sensitive to the scales of the variables involved

Mahalanobis Distance

▷Mahalanobis distance measure:

•Transforms the variables into covariance

•Make the covariance equal to 1

•Calculate simple Euclidean distance

79

)()(),( 1 yxSyxyxd

S is the covariance matrix of the input data

Similarity Between Binary Vectors

▷ Common situation is that objects, p and q, have only binary attributes

▷ Compute similarities using the following quantitiesM01 = the number of attributes where p was 0 and q was 1

M10 = the number of attributes where p was 1 and q was 0



▷ Simple Matching and Jaccard Coefficients SMC = number of matches / number of attributes

= (M11 + M00) / (M01 + M10 + M11 + M00)

J = number of 11 matches / number of not-both-zero attributes values= (M11) / (M01 + M10 + M11)

80

Cosine Similarity

▷ If d1 and d2 are two document vectors, thencos( d1, d2 ) = (d1 d2) / ||d1|| ||d2|| ,

where indicates vector dot product and || d || is the length of vector d.

▷ Example:

d1 = 3 2 0 5 0 0 0 2 0 0 d2 = 1 0 0 0 0 0 0 1 0 2

d1 d2= 3*1 + 2*0 + 0*0 + 5*0 + 0*0 + 0*0 + 0*0 + 2*1 + 0*0 + 0*2 = 5

||d1|| = (3*3+2*2+0*0+5*5+0*0+0*0+0*0+2*2+0*0+0*0)0.5 = (42) 0.5 = 6.481||d2|| = (1*1+0*0+0*0+0*0+0*0+0*0+0*0+1*1+0*0+2*2) 0.5 = (6) 0.5 = 2.245

cos( d1, d2 ) = .3150

81

Correlation

▷Correlation measures the linear relationship between objects

▷ To compute correlation, we standardize data objects, p and q,

and then take their dot product

82

)(/))(( pstdpmeanpp kk

)(/))(( qstdqmeanqq kk

qpqpncorrelatio ),(

Using Weights to Combine Similarities

▷May not want to treat all attributes the same.• Use weights wk which are between 0 and 1 and sum to 1.

83

Density

▷Density-based clustering require a notion of

density

▷Examples:• Euclidean density

→ Euclidean density = number of points per unit volume

• Probability density

• Graph-based density

84

Data Exploration

Seeing is beliving

Data Exploration

▷A preliminary exploration of the data to better

understand its characteristics

▷Key motivations of data exploration include

• Helping to select the right tool for preprocessing or

analysis

• Making use of humans’ abilities to recognize

patterns

• People can recognize patterns not captured by

data analysis tools

86

Summary Statistics

▷Summary statistics are numbers that

summarize properties of the data

•Summarized properties include frequency,

location and spread

→ Examples: location - mean

spread - standard deviation

•Most summary statistics can be calculated in

a single pass through the data

87

Frequency and Mode

▷Given a set of unordered categorical values

→ Compute the frequency with each value occurs is the

easiest way

▷The mode of a categorical attribute

• The attribute value that has the highest frequency

88

m

vvfrequency i

i

valueattribute with ovjects ofnumber

Percentiles

▷For ordered data, the notion of a percentile is

more useful

▷Given• An ordinal or continuous attribute x

• A number p between 0 and 100

▷The pth percentile xp is a value of x• p% of the observed values of x are less than xp

89

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

90

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

91

Visualization

Visualization is the conversion of data into a visual or tabular format

▷Visualization of data 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

92

Arrangement

▷Is the placement of visual elements within a display

▷Can make a large difference in how easy it is to

understand the data

▷Example

93

Visualization Techniques: Histograms

▷Histogram

• Usually shows the distribution of values of a single variable

• Divide the values into bins and show a bar plot of the number of

objects in each bin.

• The height of each bar indicates the number of objects

• Shape of histogram depends on the number of bins

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

94

Visualization Techniques: Box Plots

▷Another way of displaying the distribution of data • Following figure shows the basic part of a box plot

95

Scatter Plot Array

96

Visualization Techniques: Contour Plots

▷Contour plots • 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.

97

Celsius

Sea Surface Temperature (SST)

Visualization of the Iris Data Matrix

98

standard

deviation

Visualization of the Iris Correlation Matrix

99

Visualization Techniques: Star Plots

▷Similar approach to parallel coordinates• One axis for each attribute

▷ The size and the shape of polygon fives a visual description of the attribute value of the object

100

Petal length sepal length

Se

pa

l wid

th P

eta

l wid

th

Visualization Techniques: Chernoff Faces

▷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

101

Data Feature Facial Feature

Sepal length Size of face

Sepal width Forehead/jaw relative arc length

Petal length Shape of forehead

Petal width Shape of jaw

Do's and Don'ts

▷ Apprehension

• Correctly perceive relations among variables▷ Clarity

• Visually distinguish all the elements of a graph▷ Consistency

• Interpret a graph based on similarity to previous graphs▷ Efficiency

• Portray a possibly complex relation in as simple a way as

possible▷ Necessity

• The need for the graph, and the graphical elements▷ Truthfulness

• Determine the true value represented by any graphical

element

102

Data Mining Techniques

Yi-Shin Chen




[email protected]


mailto:yishin@

Overview

Understand the objectivities

104

Tasks in Data Mining

▷Problems should be well defined at the beginning

▷Two categories of tasks [Fayyad et al., 1996]

105

Predictive Tasks

• Predict unknown values

• e.g., potential customers

Descriptive Tasks

• Find patterns to describe data

• e.g., Friendship finding

VIPCheap

Potential

Select Techniques

▷Problems could be further decomposed

106

Predictive Tasks

• Classification

• Ranking

• Regression

• …

Descriptive Tasks

• Clustering

• Association rules

• Summarization

• …

Supervised

Learning

Unsupervised

Learning

Supervised vs. Unsupervised Learning

▷Supervised learning

• Supervision: The training data (observations, measurements,

etc.) are accompanied by labels indicating the class of the

observations

• New data is classified based on the training set

▷Unsupervised learning

• The class labels of training data is unknown

• Given a set of measurements, observations, etc. with the aim of

establishing the existence of classes or clusters in the data

107

Classification

▷Given a collection of records (training set )

• Each record contains a set of attributes

• One of the attributes is the class

▷ Find a model for class attribute:

• The model forms a function of the values of other attributes

▷Goal: previously unseen records should be assigned a class as

accurately as possible.

• A test set is needed

→ To determine the accuracy of the model

▷Usually, the given data set is divided into training & test• With training set used to build the model

• With test set used to validate it

108

Ranking

▷Produce a permutation to items in a new list• Items ranked in higher positions should be more important

• E.g., Rank webpages in a search engine Webpages in

higher positions are more relevant.

109

Regression

▷Find a function which model the data with least error• The output might be a numerical value

• E.g.: Predict the stock value

110

Clustering

▷Group data into clusters• Similar to the objects within the same cluster

• Dissimilar to the objects in other clusters

• No predefined classes (unsupervised classification)

111

Association Rule Mining

▷Basic concept• Given a set of transactions

• Find rules that will predict the occurrence of an item

• Based on the occurrences of other items in the transaction

112

Summarization

▷Provide a more compact representation of the data• Data: Visualization

• Text – Document Summarization

→ E.g.: Snippet

113

Classification

114

Illustrating Classification Task

115

Apply

Model

Induction

Deduction

Learn

Model

Model

Tid Attrib1 Attrib2 Attrib3 Class

1 Yes Large 125K No

2 No Medium 100K No

3 No Small 70K No

4 Yes Medium 120K No

5 No Large 95K Yes

6 No Medium 60K No

7 Yes Large 220K No

8 No Small 85K Yes

9 No Medium 75K No

10 No Small 90K Yes 10

Tid Attrib1 Attrib2 Attrib3 Class

11 No Small 55K ?

12 Yes Medium 80K ?

13 Yes Large 110K ?

14 No Small 95K ?

15 No Large 67K ? 10

Test Set

Learning

algorithm

Training Set

Decision Tree

116

Tid Refund MaritalStatus

TaxableIncome Cheat

1 Yes Single 125K No

2 No Married 100K No

3 No Single 70K No

4 Yes Married 120K No

5 No Divorced 95K Yes

6 No Married 60K No

7 Yes Divorced 220K No

8 No Single 85K Yes

9 No Married 75K No

10 No Single 90K Yes10

categoricalcontinuous class

© Tan, Steinbach, Kumar Introduction to Data Mining

Refund

MarSt

TaxInc

YESNO

NO

NO

Yes No

MarriedSingle, Divorced

< 80K > 80K

Splitting Attributes

Model: Decision TreeTraining Data

There could be more than one tree that fits the same data!

Algorithm for Decision Tree Induction

▷Basic algorithm (a greedy algorithm)

• Tree is constructed in a top-down recursive divide-and-conquer

manner

• At start, all the training examples are at the root

• Attributes are categorical (if continuous-valued, they are

discretized in advance)

• Examples are partitioned recursively based on selected

attributes

• Test attributes are selected on the basis of a heuristic or

statistical measure (e.g., information gain)

Data Mining 117

Tree Induction

▷Greedy strategy.

• Split the records based on an attribute test that optimizes

certain criterion.

▷Issues

• Determine how to split the records

→ How to specify the attribute test condition?

→ How to determine the best split?

• Determine when to stop splitting


The Problem Of Decision Tree

119

Deep Bushy Tree Deep Bushy Tree Useless

The Decision Tree has a hard time with correlated attributes

10

1 2 3 4 5 6 7 8 9 10

1

23456789

10

1 2 3 4 5 6 7 8 9 10

1

23456789

?100

10 20 30 40 50 60 70 80 90 100

10

20

30

40

50

60

70

80

90

Advantages/Disadvantages of Decision Trees

▷Advantages:

• Easy to understand

• Easy to generate rules

▷Disadvantages:

• May suffer from overfitting.

• Classifies by rectangular partitioning (so does not handle

correlated features very well).

• Can be quite large – pruning is necessary.

• Does not handle streaming data easily

120

Underfitting and Overfitting

121Underfitting: when model is too simple, both training and test errors are large


Overfitting due to Noise


Decision boundary is distorted by noise point

Overfitting due to Insufficient Examples


Lack of data points in the lower half of the diagram makes it difficult to

predict correctly the class labels of that region

- Insufficient number of training records in the region causes the decision

tree to predict the test examples using other training records that are

irrelevant to the classification task

Bayes Classifier

▷A probabilistic framework for solving classification

problems

▷Conditional Probability:

▷ Bayes theorem:


)(

)()|()|(

AP

CPCAPACP

)(

),()|(

)(

),()|(

CP

CAPCAP

AP

CAPACP

Bayesian Classifiers

▷Consider each attribute and class label as random

variables

▷Given a record with attributes (A1, A2,…,An)

• Goal is to predict class C

• Specifically, we want to find the value of C that maximizes

P(C| A1, A2,…,An )

▷Can we estimate P(C| A1, A2,…,An ) directly from

data?


Bayesian Classifier Approach

▷Compute the posterior probability P(C | A1, A2, …, An) for all values of C using the Bayes theorem

▷Choose value of C that maximizes P(C | A1, A2, …, An)

▷Equivalent to choosing value of C that maximizesP(A1, A2, …, An|C) P(C)

▷How to estimate P(A1, A2, …, An | C )?


)(

)()|()|(

21

2121

n

nn

AAAP

CPCAAAPAAACP

Naïve Bayes Classifier

▷A simplified assumption: attributes are conditionally

independent and each data sample has n attributes

▷No dependence relation between attributes

▷By Bayes theorem,

▷As P(X) is constant for all classes, assign X to the

class with maximum P(X|Ci)*P(Ci)

127

n

kCixkPCiXP

1

)|()|(

)()()|()|(

XPCiPCiXPXCiP

Naïve Bayesian Classifier: Comments

▷Advantages :

• Easy to implement

• Good results obtained in most of the cases

▷Disadvantages

• Assumption: class conditional independence

• Practically, dependencies exist among variables

→ E.g., hospitals: patients: Profile: age, family history etc

→ E.g., Symptoms: fever, cough etc., Disease: lung cancer, diabetes

etc

• Dependencies among these cannot be modeled by Naïve

Bayesian Classifier

▷How to deal with these dependencies?

• Bayesian Belief Networks

128

Bayesian Networks

▷Bayesian belief network allows a subset of the

variables conditionally independent

▷A graphical model of causal relationships

• Represents dependency among the variables

• Gives a specification of joint probability distribution

Data Mining 129

Bayesian Belief Network: An Example

130

Family

History

LungCancer

PositiveXRay

Smoker

Emphysema

Dyspnea

LC

~LC

(FH, S) (FH, ~S) (~FH, S) (~FH, ~S)

0.8

0.2

0.5

0.5

0.7

0.3

0.1

0.9

Bayesian Belief Networks

The conditional probability table for the variable

LungCancer:

Shows the conditional probability for each

possible combination of its parents

n

i

ZParents iziPznzP

1

))(|(),...,1(

Neural Networks

▷Artificial neuron

• Each input is multiplied by a weighting factor.

• Output is 1 if sum of weighted inputs exceeds a threshold

value; 0 otherwise

▷Network is programmed by adjusting weights using

feedback from examples

131

General Structure

Data Mining 132

Output nodes

Input nodes

Hidden nodes

Output vector

Input vector: xi

wij

i

jiijj OwI

jIje

O

1

1

))(1( jjjjj OTOOErr

jkk

kjjj wErrOOErr )1(

ijijij OErrlww )(

jjj Errl)(

Network Training

▷The ultimate objective of training • Obtain a set of weights that makes almost all the tuples in

the training data classified correctly

▷Steps• Initialize weights with random values

• Feed the input tuples into the network one by one

• For each unit

→ Compute the net input to the unit as a linear combination of

all the inputs to the unit

→ Compute the output value using the activation function

→ Compute the error

→ Update the weights and the bias

133

Summary of Neural Networks

▷Advantages

• Prediction accuracy is generally high

• Robust, works when training examples contain errors

• Fast evaluation of the learned target function

▷Criticism

• Long training time

• Difficult to understand the learned function (weights)

• Not easy to incorporate domain knowledge

134

The k-Nearest Neighbor Algorithm

▷All instances correspond to points in the n-D space.

▷The nearest neighbor are defined in terms of

Euclidean distance.

▷The target function could be discrete- or real-

valued.

▷For discrete-valued, the k-NN returns the most

common value among the k training examples

nearest to xq.

135

.

_+

_ xq

+

_ _+

_

_

+

Discussion on the k-NN Algorithm

▷Distance-weighted nearest neighbor algorithm

• Weight the contribution of each of the k neighbors

according to their distance to the query point xq

→ Giving greater weight to closer neighbors

▷Curse of dimensionality: distance between

neighbors could be dominated by irrelevant

attributes.

• To overcome it, elimination of the least relevant attributes.

136

Association Rule Mining

Definition: Frequent Itemset

▷ Itemset: A collection of one or more items

• Example: {Milk, Bread, Diaper}

▷ k-itemset

• An itemset that contains k items

▷Support count ()

• Frequency of occurrence of an itemset

• E.g. ({Milk, Bread,Diaper}) = 2

▷Support

• Fraction of transactions that contain an itemset

• E.g. s({Milk, Bread, Diaper}) = 2/5

▷ Frequent Itemset

• An itemset whose support is greater than or

equal to a minsup threshold


Market-Basket transactions

TID Items

1 Bread, Milk

2 Bread, Diaper, Beer, Eggs

3 Milk, Diaper, Beer, Coke

4 Bread, Milk, Diaper, Beer

5 Bread, Milk, Diaper, Coke

Definition: Association Rule

139

Association Rule

– An implication expression of the form

X Y, where X and Y are itemsets

– Example:

{Milk, Diaper} {Beer}

Rule Evaluation Metrics

– Support (s)

Fraction of transactions that contain

both X and Y

– Confidence (c)

Measures how often items in Y

appear in transactions that

contain X


Market-Basket transactions

Example:

Beer}Diaper,Milk{

4.05

2

|T|

)BeerDiaper,,Milk(

s

67.03

2

)Diaper,Milk(

)BeerDiaper,Milk,(

c

TID Items

1 Bread, Milk

2 Bread, Diaper, Beer, Eggs

3 Milk, Diaper, Beer, Coke

4 Bread, Milk, Diaper, Beer

5 Bread, Milk, Diaper, Coke

Strong Rules & Interesting

140

▷Corr(A,B)=P(AUB)/(P(A)P(B))• Corr(A, B)=1, A & B are independent

• Corr(A, B)<1, occurrence of A is negatively correlated with B

• Corr(A, B)>1, occurrence of A is positively correlated with B

▷E.g. Corr(games, videos)=0.4/(0.6*0.75)=0.89

• In fact, games & videos are negatively associated→ Purchase of one actually decrease the likelihood of purchasing the other

10000

6000

games

7500

video4000

Clustering Analysis

Good Clustering

▷Good clustering (produce high quality clusters)

• Intra-cluster similarity is high

• Inter-cluster class similarity is low

▷Quality factors

• Similarity measure and its implementation

• Definition and representation of cluster chosen

• Clustering algorithm

142

Types of Clusters: Well-Separated

▷Well-Separated clusters: • A cluster is a set of points such that any point in a cluster

is closer (or more similar) to every other point in the cluster than to any point not in the cluster.


3 well-separated clusters

Types of Clusters: Center-Based

▷Center-based• A cluster is a set of objects such that an object in a cluster

is closer (more similar) to the “center” of a cluster• The center of a cluster is often a centroid, the average of

all the points in the cluster, or a medoid, the most “representative” point of a cluster


4 center-based clusters

Types of Clusters: Contiguity-Based

▷Contiguous cluster (Nearest neighbor or transitive)• A cluster is a set of points such that a point in a cluster is

closer (or more similar) to one or more other points in the cluster than to any point not in the cluster.


Types of Clusters: Density-Based

▷Density-based• A cluster is a dense region of points, which is separated

by low-density regions, from other regions of high density. • Used when the clusters are irregular or intertwined, and

when noise and outliers are present.


Types of Clusters: Objective Function

▷Clusters defined by an objective function

• Finds clusters that minimize or maximize an objective

function.

• Naïve approaches:

→ Enumerate all possible ways

→ Evaluate the `goodness' of each potential set of clusters

→NP Hard

• Can have global or local objectives.

→ Hierarchical clustering algorithms typically have local

objectives

→ Partitioned algorithms typically have global objectives


Partitioning Algorithms: Basic Concept

▷Given a k, find a partition of k clusters that optimizes

the chosen partitioning criterion

• Global optimal: exhaustively enumerate all partitions.

• Heuristic methods.

→ k-means: each cluster is represented by the center of the

cluster

→ k-medoids or PAM (Partition Around Medoids) : each

cluster is represented by one of the objects in the cluster.

148

K-Means Clustering Algorithm

▷Algorithm:

• Randomly initialize k cluster means

• Iterate:

→ Assign each genes to the nearest cluster mean

→ Recompute cluster means

• Stop when clustering converges

149

K=4

Two different K-means Clusterings


-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

0

0.5

1

1.5

2

2.5

3

x

y

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

0

0.5

1

1.5

2

2.5

3

x

y

Sub-optimal Clustering

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

0

0.5

1

1.5

2

2.5

3

x

y

Optimal Clustering

Original Points

Solutions to Initial Centroids Problem

▷Multiple runs

• Helps, but probability is not on your side

▷Sample and use hierarchical clustering to determine initial

centroids

▷Select more than k initial centroids and then select among

these initial centroids

• Select most widely separated

▷Postprocessing

▷Bisecting K-means

• Not as susceptible to initialization issues


Bisecting K-means

▷ Bisecting K-means algorithm• Variant of K-means that can produce a partitioned or a

hierarchical clustering


Bisecting K-means Example

153

K=4

Bisecting K-means Example

154

K=4

Produce a hierarchical clustering based on the sequence of

clusterings produced

Limitations of K-means: Differing Sizes


Original Points K-means (3 Clusters)

One solution is to use many clusters.

Find parts of clusters, but need to put together

K-means (10 Clusters)

Limitations of K-means: Differing Density






Limitations of K-means: Non-globular Shapes






Hierarchical Clustering

▷Produces a set of nested clusters organized as a

hierarchical tree

▷Can be visualized as a dendrogram

• A tree like diagram that records the sequences of merges

or splits


1 3 2 5 4 60

0.05

0.1

0.15

0.2

1

2

3

4

5

6

1

23 4

5

Strengths of Hierarchical Clustering

▷Do not have to assume any particular number of clusters• Any desired number of clusters can be obtained by

‘cutting’ the dendogram at the proper level

▷They may correspond to meaningful taxonomies• Example in biological sciences (e.g., animal kingdom,

phylogeny reconstruction, …)


Density-Based Clustering

▷Clustering based on density (local cluster criterion),

such as density-connected points

▷Each cluster has a considerable higher density of

points than outside of the cluster

160

Density-Based Clustering Methods

▷Major features:

• Discover clusters of arbitrary shape

• Handle noise

• One scan

• Need density parameters as termination condition

▷Approaches

• DBSCAN (KDD’96)

• OPTICS (SIGMOD’99).

• DENCLUE (KDD’98)

• CLIQUE (SIGMOD’98)

Data Mining 161

DBSCAN

▷Density = number of points within a specified radius

(Eps)

▷A point is a core point if it has more than a specified

number of points (MinPts) within Eps

• These are points that are at the interior of a cluster

▷A border point has fewer than MinPts within Eps, but

is in the neighborhood of a core point

▷A noise point is any point that is not a core point or a

border point.


DBSCAN: Core, Border, and Noise Points


DBSCAN Examples


Original Points Point types: core,

border and noise

Eps = 10, MinPts = 4

When DBSCAN Works Well


Original Points Clusters

• Resistant to Noise

• Can handle clusters of different shapes and sizes

Recap: Data Mining Techniques

166

Predictive Tasks

• Classification

• Ranking

• Regression

• …

Descriptive Tasks

• Clustering

• Association rules

• Summarization

• …

Evaluation

Yi-Shin Chen




[email protected]


mailto:yishin@

Tasks in Data Mining

▷Problems should be well defined at the beginning

▷Two categories of tasks [Fayyad et al., 1996]

168

Predictive Tasks

• Predict unknown values

• e.g., potential customers

Descriptive Tasks

• Find patterns to describe data

• e.g., Friendship finding

VIPCheap

Potential

For Predictive Tasks

169

Metrics for Performance Evaluation


Focus on the predictive capability of a model

Confusion Matrix:

PREDICTED CLASS

ACTUAL

CLASS

Class=Yes Class=No

Class=Yes a b

Class=No c d

a: TP (true positive)

b: FN (false negative)

c: FP (false positive)

d: TN (true negative)

Metrics for Performance Evaluation


Most widely-used metric:

PREDICTED CLASS

ACTUAL

CLASS

Class=Yes Class=No

Class=Yes a

(TP)

b

(FN)

Class=No c

(FP)

d

(TN)

FNFPTNTP

TNTP

dcba

da

Accuracy

Limitation of Accuracy

▷Consider a 2-class problem

• Number of Class 0 examples = 9990

• Number of Class 1 examples = 10

▷ If model predicts everything to be class 0, accuracy is

9990/10000 = 99.9 %

▷Accuracy is misleading because model does not detect any

class 1 example


Cost-Sensitive Measures


cba

a

pr

rp

ba

a

ca

a

2

22(F) measure-F

(r) Recall

(p)Precision

Precision is biased towards C(Yes|Yes) & C(Yes|No)

Recall is biased towards C(Yes|Yes) & C(No|Yes)

F-measure is biased towards all except C(No|No)

dwcwbwaw

dwaw

4321

41Accuracy Weighted

Test of Significance

▷Given two models:

• Model M1: accuracy = 85%, tested on 30 instances

• Model M2: accuracy = 75%, tested on 5000 instances

▷Can we say M1 is better than M2?

• How much confidence can we place on accuracy of M1 and M2?

• Can the difference in performance measure be explained as a

result of random fluctuations in the test set?


Confidence Interval for Accuracy

▷Prediction can be regarded as a Bernoulli trial

• A Bernoulli trial has 2 possible outcomes

→ Possible outcomes for prediction: correct or wrong

• Collection of Bernoulli trials has a Binomial distribution:

→ x ≈ Bin(N, p) x: number of correct predictions

→ e.g: Toss a fair coin 50 times, how many heads would turn up?

Expected number of heads = N × p = 50 × 0.5 = 25

▷Given x (# of correct predictions) or equivalently, accuracy

(ac)=x/N, and N (# of test instances)

Can we predict p (true accuracy of model)?


Confidence Interval for Accuracy

▷For large test sets (N > 30),

• ac has a normal distribution

with mean p and variance

p(1-p)/N

• Confidence Interval for p:


Area = 1 -

Z/2 Z1- /2

1

)/)1(

( 2/12/ ZNpp

paZP c

)(2

4422

2/

22

2/2/

2

2/

ZN

aNaNZZZaNp

ccc

Example :Comparing Performance of 2 Models

▷Given: M1: n1 = 30, e1 = 0.15M2: n2 = 5000, e2 = 0.25

• d = |e2 – e1| = 0.1 (2-sided test)

▷At 95% confidence level, Z/2=1.96


0043.05000

)25.01(25.0

30

)15.01(15.0ˆ

d

128.0100.00043.096.1100.0 t

d

Interval contains 0 :

difference may not be statistically significant

For Descriptive Tasks

178

Computing Interestingness Measure

▷Given a rule X Y, information needed to compute rule

interestingness can be obtained from a contingency table


Y Y

X f11 f10 f1+

X f01 f00 fo+

f+1 f+0 |T|

Contingency table for X Y

f11: support of X and Y




Used to define various measures

support, confidence, lift, Gini,

J-measure, etc.

Drawback of Confidence


Coffee Coffee

Tea 15 5 20

Tea 75 5 80

90 10 100

Association Rule: Tea Coffee

Confidence= P(Coffee|Tea) = 0.75

but P(Coffee) = 0.9

Although confidence is high, rule is misleading

P(Coffee|Tea) = 0.9375

Statistical Independence

▷Population of 1000 students

• 600 students know how to swim (S)

• 700 students know how to bike (B)

• 420 students know how to swim and bike (S,B)

• P(SB) = 420/1000 = 0.42

• P(S) P(B) = 0.6 0.7 = 0.42

• P(SB) = P(S) P(B) => Statistical independence

• P(SB) > P(S) P(B) => Positively correlated

• P(SB) < P(S) P(B) => Negatively correlated


Statistical-based Measures

▷Measures that take into account statistical dependence


)](1)[()](1)[(

)()(),(

)()(),(

)()(

),(

)(

)|(

YPYPXPXP

YPXPYXPtcoefficien

YPXPYXPPS

YPXP

YXPInterest

YP

XYPLift

Example: Interest Factor


Coffee Coffee

Tea 15 5 20

Tea 75 5 80

90 10 100

Association Rule: Tea Coffee

Confidence= P(Coffee,Tea) = 0.15

P(Coffee) = 0.9, P(Tea) = 0.2

Interest = 0.15/(0.9×0.2)= 0.83 (< 1, therefore is negatively

associated)

Subjective Interestingness Measure

▷Objective measure:

• Rank patterns based on statistics computed from data

• e.g., 21 measures of association (support, confidence,

Laplace, Gini, mutual information, Jaccard, etc).

▷Subjective measure:

• Rank patterns according to user’s interpretation

→ A pattern is subjectively interesting if it contradicts the

expectation of a user (Silberschatz & Tuzhilin)

→ A pattern is subjectively interesting if it is actionable

(Silberschatz & Tuzhilin)


Interestingness via Unexpectedness


Need to model expectation of users (domain knowledge)

Need to combine expectation of users with evidence from data (i.e., extracted patterns)

+ Pattern expected to be frequent

- Pattern expected to be infrequent

Pattern found to be frequent

Pattern found to be infrequent

+

-

Expected Patterns-

+ Unexpected Patterns

Different Propose Measures


Some measures are

good for certain

applications, but not for

others

What criteria should we

use to determine

whether a measure is

good or bad?

Comparing Different Measures


Example f11 f10 f01 f00

E1 8123 83 424 1370

E2 8330 2 622 1046

E3 9481 94 127 298

E4 3954 3080 5 2961

E5 2886 1363 1320 4431

E6 1500 2000 500 6000

E7 4000 2000 1000 3000

E8 4000 2000 2000 2000

E9 1720 7121 5 1154

E10 61 2483 4 7452

10 examples of

contingency tables:

Rankings of contingency tables

using various measures:

Property under Variable Permutation

Does M(A,B) = M(B,A)?

Symmetric measures: support, lift, collective strength, cosine, Jaccard, etc

Asymmetric measures:

confidence, conviction, Laplace, J-measure, etc


B B A p q

A r s

A A B p r

B q s

Cluster Validity

▷ For supervised classification we have a variety of measures to

evaluate how good our model is

• Accuracy, precision, recall

▷ For cluster analysis, the analogous question is how to evaluate

the “goodness” of the resulting clusters?

▷But “clusters are in the eye of the beholder”!

▷ Then why do we want to evaluate them?

• To avoid finding patterns in noise

• To compare clustering algorithms

• To compare two sets of clusters

• To compare two clusters


Clusters Found in Random Data


0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

x

y

Random

Points

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Measures of Cluster Validity

▷Numerical measures that are applied to judge various aspects

of cluster validity, are classified into the following three types

• External Index: Used to measure the extent to which cluster

labels match externally supplied class labels, e.g., Entropy

• Internal Index: Used to measure the goodness of a clustering

structure without respect to external information, e.g., Sum of

Squared Error (SSE)

• Relative Index: Used to compare two different clusters

▷Sometimes these are referred to as criteria instead of indices

• However, sometimes criterion is the general strategy and index

is the numerical measure that implements the criterion.


Measuring Cluster Validity Via Correlation

▷ Two matrices • Proximity Matrix

• “Incidence” Matrix→ One row and one column for each data point

→ An entry is 1 if the associated pair of points belong to the same

cluster

→ An entry is 0 if the associated pair of points belongs to different

clusters

▷ Compute the correlation between the two matrices• Since the matrices are symmetric, only the correlation between

n(n-1) / 2 entries needs to be calculated.

▷ High correlation indicates that points that belong to the same

cluster are close to each other.

▷ Not a good measure for some density or contiguity based

clusters.


Measuring Cluster Validity Via Correlation

▷Correlation of incidence and proximity matrices for

the K-means clustering of the following two data sets


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Corr = -0.9235 Corr = -0.5810

Internal Measures: SSE

▷Clusters in more complicated figures aren’t well separated

▷ Internal Index: Used to measure the goodness of a clustering

structure without respect to external information

• Sum of Squared Error (SSE)

▷SSE is good for comparing two clusters

▷Can also be used to estimate the number of clusters


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Internal Measures: Cohesion and Separation

▷Cluster Cohesion: Measures how closely related are objects in

a cluster• Cohesion is measured by the within cluster sum of squares (SSE)

▷Cluster Separation: Measure how distinct or well-separated a

cluster is from other clusters• Separation is measured by the between cluster sum of squares

• Where |Ci| is the size of cluster i


i Cx

ii

mxWSS2)(

i

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Final Comment on Cluster Validity

“The validation of clustering structures is the most difficult and

frustrating part of cluster analysis.

Without a strong effort in this direction, cluster analysis will

remain a black art accessible only to those true believers who

have experience and great courage.”

Algorithms for Clustering Data, Jain and Dubes


Case Studies

Yi-Shin Chen




[email protected]


Case: Mining Reddit Data

Please check the data set during the breaks

198

Reddit Datahttps://drive.google.com/open?id=0BwpI8947eCyuRFVDLU4tT2

5JbFE

199

https://drive.google.com/open?id=0BwpI8947eCyuRFVDLU4tT25JbFE

Reddit: The Front Page of the

Internet

50k+ on

this set

Subreddit Categories

▷Reddit’s structure may already provide a

baseline similarity

Provided Data

Recover Structure

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