1. Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US CSCE 790E

2. Abstract  Introduction  Generalized Fuzzy Clustering Model  Realization  Experiment results  Conclusion

3. Introduction  What is Cluster Analysis? -- The classification of objects into categories.  Applications of Cluster Analysis: -- Pattern recognition, the classification of documents in information retrieval, social groupings based on various criteria, etc.  Why Fuzzy Clustering? -- Weaker requirements are desirable.

4. Fuzzy c-means

5. Generalized Fuzzy Clustering Model Original Objects Feature Information Fuzzy Cluster Analyzer Cluster Information Goal Objects Feature Extractor Post Treatment

6. (Cont.)  Original Objects: the representation of input data obtained by measurements on objects that are to be recognized. It may be any kind of data information in any kind of data structure.  Feature Information: characteristic features extracted from the input data in terms of which the dimensionality of pattern vectors can be reduced. The features should be characterizing attributes by which the given pattern classes are well discriminated.  Cluster Information: category information obtained through cluster analysis.  Goal Objects: Final desired result, it may not be necessary.

7. Fuzzy Cluster Analyzer Feature Data Cluster Number Exponent Initialize U^expo Distance Compute E-step M-step (f_n) (f_n x d) (c_n)(expo) U (c_n x f_n) U C (c_n x d) D (c_n x f_n) U: fuzzy partition matrix; C: center matrix; D: distance matrix. Cost

8. Realization  Initialization: Generate initial fuzzy partition matrix for clustering.  U^expo: Get the matrix after exponential modification.  E-step: Get new center matrix.  Distance compute: Calculate the distance between center and input feature data. Default: Euclidean distance.  M-step: Get new fuzzy partition matrix, and cost function value (used to control the iterations).

9. Experiment results example 1

10. Feature Data: -0.0429 -5.8091 0.0421 -6.9078 0.6455 -5.8091 -0.2485 -6.2146 -0.5465 -6.9078 -5.8091 -2.2538 -6.9078 0.5585 -4.2687 0.6092 -4.9618 0.0208 -5.5215 -1.5418 -0.5108 0 -0.1054 0.2624 0.4055 -0.3567 -1.2040 -0.1054 -0.2231 -0.5108

11. Step:0

12. Step:1

13. Step:10

14. Step:15

15. Step:20

16. Step:25

17. Result: 0.0031 0.9952 0.0017 0.0161 0.9735 0.0105 0.0230 0.9650 0.0120 0.0006 0.9991 0.0004 0.0175 0.9701 0.0124 0.0856 0.0562 0.8583 0.0829 0.0365 0.8806 0.1562 0.0343 0.8096 0.0272 0.0083 0.9645 0.0362 0.0185 0.9453 0.9942 0.0023 0.0035 0.9660 0.0141 0.0200 0.9308 0.0347 0.0345 0.9777 0.0072 0.0151 0.9788 0.0097 0.0114

18. Experiment results example 2

19. Cluster Number = 2

20. Cluster Number = 4

21. Experiment results example 3

22. Original Image Feature data(6000x3) are obtained based on texture http://vulcan.ee.iastate.edu/~dickerson/classes/ee571x/homework/hw4soln/hw4.html

23. Clustering Result

24. Conclusion  Model evaluation: –Easy to understand. –Extend applications. –Independent. –Convenient to improve.  Possible improvement involved: –Obtain Feature Data (normalization, well discriminated?) –Determine Cluster Number –U^expo (time consuming, other representation) –Distance Computation (other kind of distance)

25. Generalized Fuzzy Clustering Model Original Objects Feature Information Fuzzy Cluster Analyzer Cluster Information Goal Objects Feature Extractor Post Treatment

26. Fuzzy Cluster Analyzer Feature Data Cluster Number Exponent Initialize U^expo Distance Compute E-step M-step (f_n) (f_n x d) (c_n)(expo) U (c_n x f_n) U C (c_n x d) D (c_n x f_n) U: fuzzy partition matrix; C: center matrix; D: distance matrix. Cost