a fuzzy k-modes algorithm for clustering categorical data advisor ： dr. hsu graduate ：...

A Fuzzy k-Modes Algorithm for Clustering Categorical Data

Advisor ： Dr. Hsu

Graduate ： Chien-Ming Hsiao

Author ： Zhexue Huang and Michael K. Ng

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

Intelligent Database Systems Lab

Outline Motivation Objective Introduction Notation Hard and fuzzy k-means algorithms Hard and fuzzy k-Modes algorithms Experimental Results Conclusions Personal Opinion


Motivation

Working only on numeric data limits the use of these k-means-type algorithms in data mining.

Most algorithms for clustering categorical data suffer from a common efficiency problem when applied to massive categorical-only data sets.


Objective

To tackle the problem of clustering large categorical data sets in data mining


Introduction

Fuzzy versions of k-means algorithm

Each pattern is allowed to have membership functions to all clusters.

Working only on numeric data limits the use of these k-means-type algorithms in such areas data mining.


Introduction

To cluster categorical data methods

the k-means algorithm [Ralambondrainy, 1995] hierarchical clustering methods [Gower, 1991] the PAM algorithm [Kaufman et al, 1990] the fuzzy-statistical algorithms [Woodbury, 1974] The conceptual clustering methods [Michalski, 1983]


Notation The set of objects to be clustered is stored in a database

table T defined by a set of attributes A1, A2,…, Am.

objects. ofset a be XLet 21 n,X,,XX n

.,,, as drepresente is Object 21i i,mi,i, xxxX


Hard and fuzzy k-means algorithms

Let X be a set of n objects described by m numeric attributes.



The usual method toward optimization of F is to use partial optimization for Z and W

fix Z and find necessary conditions on W to minimize F Fix W and minimize F with respect to Z



Theorem 1 Let be fixed and consider Problem (P1)



Theorem 2 Let be fixed and consider Problem (P2)



The complexity of the algorithm O(tkmn)

The space of the algorithm O(n(m+k) + km)


Hard and fuzzy k-Modes algorithms

Using a simple matching dissimilarity measure for categorical objects

Replacing the means of clusters with the modes

Using a frequency-based method to find the modes



Let X and Y be two categorical objects X = Y =

The simple matching dissimilarity measure between X and Y is defined as follows:



Using a frequency-based method to update Z

The Hard k-modes Update Method

The Fuzzy k-modes Update Method



Theorem 3 : The Hard k-modes Update Method The category of attribute Aj of the cluster mode Zl is det

ermined by the mode of categories of attribute Aj in the set of objects belonging to cluster l

the quantity



Theorem 4 : The Fuzzy k-modes Update Method The category of attribute Aj of the cluster mode Zl is giv

en by the category that achieves the maximum of the summation of wli to cluster l over all categories.

the quantity



Theorem 5

.iterations ofnumber finite ain converges

algorithm modes-kfuzzy The 1. Let


Experimental Results To evaluate the performance and efficiency of the

fuzzy k-modes algorithm

To compare the fuzzy k-modes algorithm with the conceptual k-means algorithm and the hard k-modes algorithm

Use real and artificial data Soybean disease data set.


Experimental Results


Conclusions

Introduced the fuzzy k-modes algorithm for clustering categorical objects based on extensions to the fuzzy k-means algorithm.

The consequence of Theorem 4 that allows the k-means paradigm to be used in generating the fuzzy partition matrix from categorical data


Personal Opinion

The fuzzy partition matrix provides more information to help the user to determine the final clustering and to identify the boundary objects

a fuzzy k-modes algorithm for clustering categorical data advisor ： dr. hsu graduate ：...

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