Transcript No Slide Title

Data Mining:
Concepts and Techniques
— Slides for Textbook —
— Chapter 8 —
©Jiawei Han and Micheline Kamber
Department of Computer Science
University of Illinois at Urbana-Champaign
www.cs.uiuc.edu/~hanj
July 17, 2015
Data Mining: Concepts and Techniques
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Cluster Analysis

What is Cluster Analysis?

Types of Data in Cluster Analysis

A Categorization of Major Clustering Methods

Hierarchical Methods
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Data Mining: Concepts and Techniques
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What is Cluster Analysis?
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Cluster: a collection of data objects
 Similar to one another within the same cluster
 Dissimilar to the objects in other clusters
Cluster analysis
 Grouping a set of data objects into clusters
Clustering is unsupervised classification: no predefined
classes
Typical applications
 As a stand-alone tool to get insight into data
distribution
 As a preprocessing step for other algorithms
General Applications of Clustering
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Pattern Recognition
Spatial Data Analysis
 create thematic maps in GIS by clustering feature
spaces
 detect spatial clusters and explain them in spatial data
mining
Image Processing
Economic Science (especially market research)
WWW
 Document classification
 Cluster Weblog data to discover groups of similar
access patterns
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Data Mining: Concepts and Techniques
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Examples of Clustering Applications
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Marketing: Help marketers discover distinct groups in
their customer bases, and then use this knowledge to
develop targeted marketing programs
Land use: Identification of areas of similar land use in an
earth observation database
Insurance: Identifying groups of motor insurance policy
holders with a high average claim cost
City-planning: Identifying groups of houses according to
their house type, value, and geographical location
Earth-quake studies: Observed earth quake epicenters
should be clustered along continent faults
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Data Mining: Concepts and Techniques
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What Is Good Clustering?
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A good clustering method will produce high quality
clusters with
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high intra-class similarity
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low inter-class similarity
The quality of a clustering result depends on both the
similarity measure used by the method and its
implementation.
The quality of a clustering method is also measured by its
ability to discover some or all of the hidden patterns.
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Data Mining: Concepts and Techniques
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Requirements of Clustering in Data
Mining
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Scalability
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Ability to deal with different types of attributes
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Discovery of clusters with arbitrary shape
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Minimal requirements for domain knowledge to
determine input parameters
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Able to deal with noise and outliers
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Insensitive to order of input records
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High dimensionality
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Incorporation of user-specified constraints
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Interpretability and usability
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Data Mining: Concepts and Techniques
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Cluster Analysis

What is Cluster Analysis?

Types of Data in Cluster Analysis

A Categorization of Major Clustering Methods

Hierarchical Methods
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Data Mining: Concepts and Techniques
8
Data Structures
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Data matrix
 (two modes)
 x 11

 ...
 x
 i1
 ...
x
 n1
Dissimilarity matrix
 (one mode)
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 0

d(2,1)

 d(3,1 )

:

 d ( n ,1 )

...
x
...
...
x
if
...
...
...
1f
...
x
nf
1p 

... 
x 
ip 
... 

x
np 
...
x
...
...
...
...
0
d ( 3 ,2 )
0
:
:
d ( n ,2 )
...
Data Mining: Concepts and Techniques
...






0 
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Measure the Quality of Clustering
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Dissimilarity/Similarity metric: Similarity is expressed in
terms of a distance function, which is typically metric:
d(i, j)
There is a separate “quality” function that measures the
“goodness” of a cluster.
The definitions of distance functions are usually very
different for interval-scaled, boolean, categorical, ordinal
and ratio variables.
Weights should be associated with different variables
based on applications and data semantics.
It is hard to define “similar enough” or “good enough”

the answer is typically highly subjective.
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Data Mining: Concepts and Techniques
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Type of data in clustering analysis
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Interval-scaled variables:
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Binary variables:
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Nominal, ordinal, and ratio variables:
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Variables of mixed types:
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Data Mining: Concepts and Techniques
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Interval-valued variables
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Standardize data
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Calculate the mean absolute deviation:
s f  1n (| x1 f  m f |  | x 2 f  m f |  ...  | x nf  m f |)
where
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m f  1 (x 1 f  x 2 f
n
x nf
).
Calculate the standardized measurement (z-score)
z if 

 ... 
x m
if
s
f
f
Using mean absolute deviation is more robust than using
standard deviation
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Data Mining: Concepts and Techniques
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Similarity and Dissimilarity Between
Objects
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Distances are normally used to measure the similarity or
dissimilarity between two data objects
Some popular ones include: Minkowski distance:
q
q
q
d (i , j )  q (| x  x |  | x  x |  ...  | x  x | )
i1
j1
i2
j2
ip
jp
where i = (xi1, xi2, …, xip) and j = (xj1, xj2, …, xjp) are
two p-dimensional data objects, and q is a positive
integer

If q = 1, d is Manhattan distance
d (i, j ) | x  x |  | x  x |  ...  | x  x |
i1 j 1
i2
j2
ip
jp
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Data Mining: Concepts and Techniques
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Similarity and Dissimilarity Between
Objects (Cont.)
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If q = 2, d is Euclidean distance:
d (i , j ) 
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Properties
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(| x  x |  | x  x |  ...  | x  x | )
i1
j1
i2
j2
ip
jp
2
2
2
d(i,j)  0
d(i,i) = 0
d(i,j) = d(j,i)
d(i,j)  d(i,k) + d(k,j)
Also, one can use weighted distance, parametric
Pearson product moment correlation, or other
disimilarity measures
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Data Mining: Concepts and Techniques
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Binary Variables
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A contingency table for binary data
Object j
Object i
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1
0
sum
1
a
b
ab
0
c
d
cd
sum
ac
bd
p
Simple matching coefficient (invariant, if the binary
variable is symmetric):
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d (i , j ) 
bc
abcd
Jaccard coefficient (noninvariant if the binary variable is
asymmetric):
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d (i , j ) 
bc
abc
Data Mining: Concepts and Techniques
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Dissimilarity between Binary
Variables
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Example
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N am e G ender Fever C ough T est-1
T est-2
T est-3
T est-4
Jack
M ary
Jim
N
N
N
N
P
N
N
N
N
M
F
M
Y
Y
Y
N
N
P
P
P
N
gender is a symmetric attribute
the remaining attributes are asymmetric binary
let the values Y and P be set to 1, and the value N be set to 0
d ( jack , mary ) 
d ( jack , jim ) 
d ( jim , mary ) 
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0  1
2  0  1
1 1
1 1 1
1 2
1 1 2
 0 . 33
 0 . 67
 0 . 75
Data Mining: Concepts and Techniques
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Nominal Variables
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A generalization of the binary variable in that it can take
more than 2 states, e.g., red, yellow, blue, green
Method 1: Simple matching
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m : # of matches, p : total # of variables
d (i , j ) 
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pm
p
Method 2: use a large number of binary variables
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creating a new binary variable for each of the M
nominal states
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Data Mining: Concepts and Techniques
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Ordinal Variables
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An ordinal variable can be discrete or continuous
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Order is important, e.g., rank
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Can be treated like interval-scaled
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f
}
map the range of each variable onto [0, 1] by replacing
i-th object in the f-th variable by
z if 
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rif  {1,..., M
replace xif by their rank
rif  1
M
f
1
compute the dissimilarity using methods for intervalscaled variables
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Ratio-Scaled Variables
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Ratio-scaled variable: a positive measurement on a
nonlinear scale, approximately at exponential scale,
such as AeBt or Ae-Bt
Methods:
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treat them like interval-scaled variables—not a good
choice! (why?—the scale can be distorted)
apply logarithmic transformation
yif = log(xif)
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treat them as continuous ordinal data treat their rank
as interval-scaled
Data Mining: Concepts and Techniques
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Variables of Mixed Types
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A database may contain all the six types of variables
 symmetric binary, asymmetric binary, nominal,
ordinal, interval and ratio
One may use a weighted formula to combine their
effects
 pf  1 ij( f ) d ij( f )
d (i , j ) 
 pf  1 ij( f )
 f is binary or nominal:
dij(f) = 0 if xif = xjf , or dij(f) = 1 o.w.
 f is interval-based: use the normalized distance
 f is ordinal or ratio-scaled
 compute ranks rif and
r 1
z

if
 and treat zif as interval-scaled
M 1
if
f
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Cluster Analysis

What is Cluster Analysis?

Types of Data in Cluster Analysis

A Categorization of Major Clustering Methods

Hierarchical Methods
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Data Mining: Concepts and Techniques
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Major Clustering Approaches
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Hierarchy algorithms: create a hierarchical decomposition
of the set of data (or objects) using some criterion
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Partitioning algorithms: construct various partitions and
then evaluate them by some criterion
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Density-based: based on connectivity and density functions
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Grid-based: based on a multiple-level granularity structure
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Model-based: a model is hypothesized for each of the
clusters and the idea is to find the best fit of that model to
each other
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Data Mining: Concepts and Techniques
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Cluster Analysis

What is Cluster Analysis?

Types of Data in Cluster Analysis

A Categorization of Major Clustering Methods

Hierarchical Methods
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Hierarchical Clustering
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Use distance matrix as clustering criteria. This method
does not require the number of clusters k as an input,
but needs a termination condition
Step 0
a
Step 1
Step 2 Step 3 Step 4
agglomerative
(AGNES)
ab
b
abcde
c
cde
d
de
e
Step 4
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Step 3
Step 2 Step 1 Step 0
Data Mining: Concepts and Techniques
divisive
(DIANA)
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AGNES (Agglomerative Nesting)
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Introduced in Kaufmann and Rousseeuw (1990)
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Implemented in statistical analysis packages, e.g., Splus
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Use the Single-Link method and the dissimilarity matrix.
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Merge nodes that have the least dissimilarity
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Go on in a non-descending fashion
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Eventually all nodes belong to the same cluster
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A Dendrogram Shows How the
Clusters are Merged Hierarchically
Decompose data objects into a several levels of nested
partitioning (tree of clusters), called a dendrogram.
A clustering of the data objects is obtained by cutting the
dendrogram at the desired level, then each connected
component forms a cluster.
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Data Mining: Concepts and Techniques
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DIANA (Divisive Analysis)
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Introduced in Kaufmann and Rousseeuw (1990)
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Implemented in statistical analysis packages, e.g., Splus
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Inverse order of AGNES
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Eventually each node forms a cluster on its own
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More on Hierarchical Clustering Methods
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Major weakness of agglomerative clustering methods
2
 do not scale well: time complexity of at least O (n ),
where n is the number of total objects
 can never undo what was done previously
Integration of hierarchical with distance-based clustering
 BIRCH (1996): uses CF-tree and incrementally adjusts
the quality of sub-clusters
 CURE (1998): selects well-scattered points from the
cluster and then shrinks them towards the center of the
cluster by a specified fraction
 CHAMELEON (1999): hierarchical clustering using
dynamic modeling
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Data Mining: Concepts and Techniques
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CHAMELEON (Hierarchical clustering
using dynamic modeling)
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CHAMELEON: by G. Karypis, E.H. Han, and V. Kumar’99
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Measures the similarity based on a dynamic model
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Two clusters are merged only if the interconnectivity and closeness
(proximity) between two clusters are high relative to the internal
interconnectivity of the clusters and closeness of items within the
clusters
Cure ignores information about interconnectivity of the objects,
Rock ignores information about the closeness of two clusters
A two-phase algorithm
1. Use a graph partitioning algorithm: cluster objects into a large
number of relatively small sub-clusters
2. Use an agglomerative hierarchical clustering algorithm: find the
genuine clusters by repeatedly combining these sub-clusters
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Data Mining: Concepts and Techniques
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Overall Framework of CHAMELEON
Construct
Partition the Graph
Sparse Graph
Data Set
Merge Partition
Final Clusters
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Data Mining: Concepts and Techniques
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