Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US CSCE 790E CSCE 790E
Generalized Fuzzy Clustering Model
with Fuzzy C-Means Hong Jiang
Computer Science and Engineering, University of South Carolina,
Columbia, SC 29208, US
CSCE 790ECSCE 790E
Abstract Introduction Generalized Fuzzy Clustering
Model Realization Experiment results Conclusion
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.
Fuzzy c-means
Generalized Fuzzy Clustering Model
Original Objects
Original Objects
Feature Information
Feature Information
Fuzzy Cluster Analyzer
Fuzzy Cluster Analyzer
Cluster Information
Cluster Information
Goal Objects Goal
Objects
Feature ExtractorFeature
ExtractorPost
TreatmentPost
Treatment
(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.
Fuzzy Cluster AnalyzerFeature
DataCluster Number
Exponent
Initialize U^expo
DistanceCompute
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
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).
Experiment results
example 1
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
Step: 0
Step: 1
Step: 10
Step: 15
Step: 20
Step: 25
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
Experiment results
example 2
Cluster Number = 2
Cluster Number = 4
Experiment results
example 3
Original Image
Feature data(6000x3) are obtained based on texturehttp://vulcan.ee.iastate.edu/~dickerson/classes/ee571x/homework/hw4soln/hw4.html
Clustering Result
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)
Generalized Fuzzy Clustering Model
Original Objects
Original Objects
Feature Information
Feature Information
Fuzzy Cluster Analyzer
Fuzzy Cluster Analyzer
Cluster Information
Cluster Information
Goal Objects Goal
Objects
Feature ExtractorFeature
ExtractorPost
TreatmentPost
Treatment
Fuzzy Cluster AnalyzerFeature
DataCluster Number
Exponent
Initialize U^expo
DistanceCompute
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