1. A Fuzzy k-Modes Algorithm for Clustering Categorical Data
國立雲林科技大學 National Yunlin University of Science and Technology
A Fuzzy k-Modes Algorithm for Clustering Categorical Data
Advisor：Dr. Hsu
Graduate：Chien-Ming Hsiao
Author：Zhexue Huang and Michael K. Ng

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

3. 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.

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

5. 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.

6. 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]

7. Notation
The set of objects to be clustered is stored in a database table T defined by a set of attributes A1, A2,…, Am.

8. Hard and fuzzy k-means algorithms
Let X be a set of n objects described by m numeric attributes.

9. Hard and fuzzy k-means algorithms
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

10. Hard and fuzzy k-means algorithms
Theorem 1
Let be fixed and consider Problem (P1)

11. Hard and fuzzy k-means algorithms
Theorem 2
Let be fixed and consider Problem (P2)

12. Hard and fuzzy k-means algorithms
The complexity of the algorithm
O(tkmn)
The space of the algorithm
O(n(m+k) + km)

13. 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

14. Hard and fuzzy k-Modes algorithms
Let X and Y be two categorical objects
X =
Y =
The simple matching dissimilarity measure between X and Y is defined as follows:

15. Hard and fuzzy k-Modes algorithms
Using a frequency-based method to update Z
The Hard k-modes Update Method
The Fuzzy k-modes Update Method

16. Hard and fuzzy k-Modes algorithms
Theorem 3 : The Hard k-modes Update Method
The category of attribute Aj of the cluster mode Zl is determined by the mode of categories of attribute Aj in the set of objects belonging to cluster l
the quantity

18. Hard and fuzzy k-Modes algorithms
Theorem 4 : The Fuzzy k-modes Update Method
The category of attribute Aj of the cluster mode Zl is given by the category that achieves the maximum of the summation of wli to cluster l over all categories.
the quantity

20. Hard and fuzzy k-Modes algorithms
Theorem 5

21. Hard and fuzzy k-Modes algorithms

22. 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.

23. Experimental Results

24. Experimental Results

25. Experimental Results

26. Experimental Results

27. Experimental Results

28. 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

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