CS281B Winter02
Yan Wang and Lihua Lin
1
K

means clustering
CS281B Winter02
Yan Wang and Lihua Lin
2
What are clustering algorithms?
What is clustering ?
Clustering of data is a method by which large sets of data is
grouped into clusters of smaller sets of similar data.
Example:
The balls of same color are clustered into a group as shown
below :
Thus, we see clustering means grouping of data or dividing a
large data set into smaller data sets of some similarity.
CS281B Winter02
Yan Wang and Lihua Lin
3
What is a clustering algorithm ?
A clustering algorithm attempts to find natural groups of
components (or data) based on some similarity.
The clustering algorithm also finds the
centroid
of a group of
data sets.
The
centroid
of a cluster is a point whose parameter values are
the mean of the parameter values of all the points in the
clusters.
CS281B Winter02
Yan Wang and Lihua Lin
4
What is the common metric for clustering techniques ?
Generally, the
distance between two points
is taken as a
common metric to assess the similarity among the components
of a population. The most commonly used distance measure is
the
Euclidean metric
which defines the distance between two
points
p
= (
p
1
,
p
2
, ....) and
q
= (
q
1
,
q
2
, ....) as :
2
1
)
(
i
k
i
i
q
p
d
CS281B Winter02
Yan Wang and Lihua Lin
5
Uses of clustering algorithms
Engineering sciences: pattern recognition, artificial intelligence,
cybernetics etc. Typical examples to which clustering has been
applied include handwritten characters, samples of speech,
fingerprints, and pictures.
Life sciences (biology, botany, zoology, entomology, cytology,
microbiology): the objects of analysis are life forms such as
plants, animals, and insects.
Information, policy and decision sciences: the various
applications of clustering analysis to documents include votes
on political issues, survey of markets, survey of products, survey
of sales programs, and R & D.
CS281B Winter02
Yan Wang and Lihua Lin
6
Types of clustering algorithms
The various clustering
concepts available can be
grouped into two broad
categories :
Hierarchial methods
–
Minimal Spanning Tree
Method (Fig)
Nonhierarchial methods
–
K

means Algorithm
CS281B Winter02
Yan Wang and Lihua Lin
7
K

Means Clustering Algorithm
Definition:
This nonheirarchial method initially takes the number of
components of the population equal to the final required
number of clusters. In this step itself the final required
number of clusters is chosen such that the points are
mutually farthest apart. Next, it examines each component in
the population and assigns it to one of the clusters
depending on the minimum distance. The centroid's position
is recalculated everytime a component is added to the
cluster and this continues until all the components are
grouped into the final required number of clusters.
CS281B Winter02
Yan Wang and Lihua Lin
8
K

Means Clustering Algorithm
CS281B Winter02
Yan Wang and Lihua Lin
9
The Parameters and options for the k

means algorithm
•
Initialization
: Different init Methods
•
Distance Measure
:There are different distance measures that
can be used. (Manhattan distance & Euclidean distance).
•
Termination
: k

means should terminate when no more pixels
are changing classes.
•
Quality
: the quality of the results provided by k

means
classification
•
Parallelism
: There are several ways to parallelize the k

means
algorithm
•
What to do with dead classes
:A class is "dead" if no pixels
belong to it.
•
Variants
: one pass on

the

fly calculation of means
•
Number of classes
: Number of classes is usually given as an
input variable.
CS281B Winter02
Yan Wang and Lihua Lin
10
Comments on the K

means Methods
Strength of the K

means:
•
Relatively efficient:
O(tkn),
where
n
is the number of objects,
k
is the number of clusters, and
t
is number of iterations.
Normally,
k,t << n
.
•
Often terminates at a local optimum.
Weakness of the k

means:
•
Applicable only when mean is defined, then what about
categorical data?
•
Need to specify
k
, the number of clusters, in advance.
•
Unable tom handle noisy data and outlines.
•
Not suitable to discover clusters with non

convex shapes.
CS281B Winter02
Yan Wang and Lihua Lin
11
Direct k

means clustering algorithm
CS281B Winter02
Yan Wang and Lihua Lin
12
2 Initial
Clusters
Demo (I)
CS281B Winter02
Yan Wang and Lihua Lin
13
2

means
Clustering
Demo (I)
CS281B Winter02
Yan Wang and Lihua Lin
14
Demo (II)
–
Init Method: Random
CS281B Winter02
Yan Wang and Lihua Lin
15
Demo (II)
–
Init Method: Linear
CS281B Winter02
Yan Wang and Lihua Lin
16
Demo (II)
–
Init Method: Cube
CS281B Winter02
Yan Wang and Lihua Lin
17
Demo (II)
–
Init Method: Statistics
CS281B Winter02
Yan Wang and Lihua Lin
18
Demo (II)
–
Init Method: Possibility
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