A genetic clustering algorithm for data with non-spherical-shape clusters

1Intelligent Database Systems Lab

國立雲林科技大學National Yunlin University of Science and Technology

Advisor ： Dr. Hsu Graduate ： Sheng-Hsuan Wang Authors ： Lin Yu Tseng

Shiueng Bien Yang

Department of Information Management

Pattern Recognition 33 (2000) 1251-1259

Intelligent Database Systems Lab

N.Y.U.S.T.

Outline

Motivation Objective Introduction The basic concept of genetic strategy The genetic clustering algorithm Experiments Concluding remarks and Summary Personal opinions Review

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Motivation

Some problems of the clustering. The number of clusters? The threshold distance d in neighborhood clustering. Non-spherical-shape clusters.

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Objective

To solve the problem of these traditional clustering algorithm.

A genetic clustering algorithm for clustering. Non-spherical-shape clusters. According to the similarities and automatically find the pr

oper k.

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Introduction

These clustering methods can broadly be classified into two categories: Hierarchical

agglomerative divisive

Non-hierarchical k-means

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Introduction

The problems in most of these clustering algorithms The number of clusters? Non-spherical shape cluster? The threshold of distance for merge?

GA clustering algorithm Searching, as same as clustering.

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Basic concept of Classical Genetic Algorithm

Encoding schemas

Fitness evaluation

Testing the end of the algorithm

Parent selection

Crossover operators

Mutation operators

NO Halt

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The genetic clustering algorithm

The algorithm CLUSTERING consists of two stages

First stage

Nearest Neighbor

C1, C2, …, Cm

n objects,

O1, O2, …, On

Second stage

GA clustering

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First Stage

Step 1: find the nearest neighbor of each object Oi.

Step 2: dav, the average of the nearest neighbor distances.

The mean of u ?

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First Stage

Step 3: compute the adjacency matrix Anxn.

Step 4: connected components be denoted by

C1, C2, …, Cm.

otherwise

dOOifjiA ji

1 where

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Second Stage

The initialization step Population Coding Dinter and Dintra

The three phases of GA Reproduction phase Crossover phase Mutation phase

Encoding schemas

Fitness evaluation

Testing the end of the algorithm

Parent selection

Crossover operators

Mutation operators

NO Halt

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Second Stage

Distance matrix Dmxm of each pair of cluster Ci and Cj.

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Second Stage

The initialization step Population: 50 strings. The length of each string is m:

{C1, C2, …, Cm}

For each string Ri, two sets Ui and U’i are defined

1 1 1 0 0

1 0 1 1 0

U1={C1, C2, C3} ; U’1={C4, C5}

U2={C1, C3, C4} ; U’2={C2, C5}

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Second Stage

Intra-distance Dintra and the inter-distance Dinter

U1={C1, C2, C3} ; U’1={C4, C5, C7}

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Second Stage

Reproduction phase Fitness function

SCORE(Ri) = Dinter(Ri)*w – Dintra(Ri), w within [1,3]. Reproducted probability

Crossover phase pc = 0.8.

Mutation phase pm = 0.1.

R1 1 1 1 0 0R2 1 0 1 1 0

iii RSCORERSCORE

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Merge_Sets_Finding Algorithm

Step 1: Sort the fitness of the strings.

Step 2: Choose Ri.

Step 3: Choose smallest l > i such that .IF no such l exists THEN go to Step 4(discarded)

ELSE i = l and go to Step 2(merge)

Step 4: End.

)(...)()( 21 NRSCORERSCORERSCORE

R1={C1, C2, C3}

R2={C3, C4, C6}

R3={C4, C5}iUUU

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Experiments - 1

Noise : distance > 2dav

Original

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Experiments - 1

u=1.2, 8 clusters

7 clusters

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Experiments - 1

6 clusters u=1.5 or 2, 5 clusters

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Experiments - 1

u=1.2, w=2,

4 clusters (best)

3 clusters

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Experiments - 1

2 clusters 4 clusters (direct GA)

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Experiments - 1

4 clusters (k-mean)

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Experiments - 2

Original

4 clusters

3 clusters

2 clusters

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Experiments - 3

Original

4 clusters

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Concluding and Summary

A genetic clustering algorithm CLUSTERING Non-spherical shape. Automatic clustering. Binary searching the proper interval for w.

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Personal Opinions The proper number of cluster decide by the value of w.

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Review

Using GCA to automatic clustering. Split : NN. Merge : Merge_Sets_Finding Algorithm.

A genetic clustering algorithm for data with non-spherical-shape clusters

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