Quick Guide to Data Mining Concepts

Quick Tour of Data Mining
Yi-Shin Chen
Institute of Information Systems and Applications
Department of Computer Science
National Tsing Hua University
yishin@gmail.com

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 processing
Punched-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 Chen
1993: 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 Cleaning
Data Integration
Databases
Data
Warehouse
Task-relevant
Data
Selection
Data Mining
Pattern
Evaluation

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 Cleaning
Data 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
ThicknessLoadDistanceProjection
of y load
Projection
of x Load
1.12.216.226.2512.65
1.22.715.225.2710.23
ThicknessLoadDistanceProjection
of y load
Projection
of x Load
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 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

Data Matrix/Graph Data Example
22

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
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

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 =
𝑛 𝑖𝑗
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 = 𝑙𝑜𝑔
𝑁
𝑑𝑓 𝑖
+ 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

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

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
Waves
Two Sine Waves +
Noise Frequency

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(Frequency)
Log(Log(Frequency))

Data Collection
▷Align /Classify the attributes correctly
60
Who post this message Mentioned User
Hashtag
Shared URL

Language Detection
▷To detect an language (possible languages)
in which the specified text is written
▷Difficulties
•Short message
•Different languages in one statement
•Noisy
61
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 €, £, $...
Tweet URL
Filter out non-(letters, space,
punctuation, digit) ◕‿◕ Friendship is everything ♥ ✉
xxxx@gmail.com
I added a video to a @YouTube playlist
http://t.co/ceYX62StGO Jamie Riepe
(^|s*)http(S+)?(s*|$)
(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
k
kk 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
r
n
k
r
kk 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 quantities
M01 = the number of attributes where p was 0 and q was 1
▷ 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, then
cos( 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
v
vfrequency i
i
valueattributewithovjectsofnumber


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

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
SepalwidthPetalwidth

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
yishin@gmail.com

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
VIP
Cheap
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

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 Marital
Status
Taxable
Income 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 Yes
10
categorical
continuous class
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
118

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
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
7
8
9
?
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
121
Underfitting: when model is too simple, both training and test errors are large

Overfitting due to Noise
122
Decision boundary is distorted by noise point

Overfitting due to Insufficient Examples
123
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:
124
)(
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AP
CPCAP
ACP 
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),(
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CP
CAP
CAP
AP
CAP
ACP
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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?
125

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 maximizes
P(A1, A2, …, An|C) P(C)
▷How to estimate P(A1, A2, …, An | C )?
126
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21
21
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n
n
AAAP
CPCAAAP
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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
k
CixkPCiXP
1
)|()|(
)(
)()|()|(
XP
CiPCiXPXCiP 

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 
jIj
e
O 


1
1
))(1( jjjjj OTOOErr 
jk
k
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

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
138
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{ 
4.0
5
2
|T|
)BeerDiaper,,Milk(


s
67.0
3
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

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.
143
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
144
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.
145

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.
146

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
147

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
150
-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
151

Bisecting K-means
▷ Bisecting K-means algorithm
• Variant of K-means that can produce a partitioned or a
hierarchical clustering
152

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
155
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
156

Limitations of K-means: Non-globular Shapes
157

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
158
1 3 2 5 4 6
0
0.05
0.1
0.15
0.2
1
2
3
4
5
6
1
2
3 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, …)
159

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.
162

DBSCAN: Core, Border, and Noise Points
163

DBSCAN Examples
164
Original Points Point types: core,
border and noise
Eps = 10, MinPts = 4

When DBSCAN Works Well
165
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
yishin@gmail.com

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
VIP
Cheap
Potential

Metrics for Performance Evaluation
170
 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
171
 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
172

Cost-Sensitive Measures
173
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a
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a
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
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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
41
AccuracyWeighted

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

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?
174

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)?
175

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:
176
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Example :Comparing Performance of 2 Models
▷Given: M1: n1 = 30, e1 = 0.15
M2: n2 = 5000, e2 = 0.25
• d = |e2 – e1| = 0.1 (2-sided test)
▷At 95% confidence level, Z/2=1.96
177
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5000
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d
Interval contains 0 :
difference may not be statistically significant

Computing Interestingness Measure
▷ Given a rule X  Y, information needed to compute rule
interestingness can be obtained from a contingency table
179
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
180
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(SB) = 420/1000 = 0.42
• P(S)  P(B) = 0.6  0.7 = 0.42
• P(SB) = P(S)  P(B) => Statistical independence
• P(SB) > P(S)  P(B) => Positively correlated
• P(SB) < P(S)  P(B) => Negatively correlated
181

Statistical-based Measures
▷Measures that take into account statistical dependence
182
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Lift








Example: Interest Factor
183
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)
184

Interestingness via Unexpectedness
185
 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
186
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
187
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
188
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
189

Clusters Found in Random Data
190
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
y
Random
Points
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
y
K-
means
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
y
DBSCAN
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
y
Complete
Link

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.
191

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.
192

Measuring Cluster Validity Via Correlation
▷Correlation of incidence and proximity matrices for
the K-means clustering of the following two data sets
193
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
y
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
y
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
194
2 5 10 15 20 25 30
0
1
2
3
4
5
6
7
8
9
10
K
SSE
5 10 15
-6
-4
-2
0
2
4
6

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
195
 


i Cx
i
i
mxWSS 2
)(
 
i
ii mmCBSS 2
)(

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
196

Case Studies
Yi-Shin Chen
yishin@gmail.com

Case: Mining Reddit Data
Please check the data set during the breaks
198

Reddit Data
https://drive.google.com/open?id=0BwpI8947eCyuRFVDLU4tT2
5JbFE
199

Reddit: The Front Page of the
Internet
50k+ on
this set

Subreddit Categories
▷Reddit’s structure may already provide a
baseline similarity

Quick Guide to Data Mining Concepts

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