generalized fuzzy clustering model with fuzzy c-means hong jiang computer science and engineering,...
TRANSCRIPT
![Page 1: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/1.jpg)
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
![Page 2: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/2.jpg)
Abstract Introduction Generalized Fuzzy Clustering
Model Realization Experiment results Conclusion
![Page 3: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/3.jpg)
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.
![Page 4: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/4.jpg)
Fuzzy c-means
![Page 5: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/5.jpg)
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
![Page 6: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/6.jpg)
(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.
![Page 7: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/7.jpg)
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
![Page 8: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/8.jpg)
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).
![Page 9: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/9.jpg)
Experiment results
example 1
![Page 10: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/10.jpg)
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
![Page 11: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/11.jpg)
Step: 0
![Page 12: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/12.jpg)
Step: 1
![Page 13: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/13.jpg)
Step: 10
![Page 14: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/14.jpg)
Step: 15
![Page 15: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/15.jpg)
Step: 20
![Page 16: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/16.jpg)
Step: 25
![Page 17: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/17.jpg)
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
![Page 18: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/18.jpg)
Experiment results
example 2
![Page 19: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/19.jpg)
Cluster Number = 2
![Page 20: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/20.jpg)
Cluster Number = 4
![Page 21: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/21.jpg)
Experiment results
example 3
![Page 22: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/22.jpg)
Original Image
Feature data(6000x3) are obtained based on texturehttp://vulcan.ee.iastate.edu/~dickerson/classes/ee571x/homework/hw4soln/hw4.html
![Page 23: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/23.jpg)
Clustering Result
![Page 24: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/24.jpg)
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)
![Page 25: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/25.jpg)
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
![Page 26: Generalized Fuzzy Clustering Model with Fuzzy C-Means Hong Jiang Computer Science and Engineering, University of South Carolina, Columbia, SC 29208, US](https://reader035.vdocument.in/reader035/viewer/2022062423/56649ecf5503460f94bdcef1/html5/thumbnails/26.jpg)
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