Clustering analysis and selforganization Clustering analysis v Hierarchical

Clustering analysis and self-organization Ø Clustering analysis v Hierarchical algorithm v Partitioning algorithm Ø Self-organization v Kohonen self-organizing algorithm v Elastic nets v Slef-organization using Potts models v Natural elastic nets using Potts models Intelligent Numerical Computation 1

Internet resources: Mixture models: http: //www. csse. monash. edu. au/~dld/mixture. modelling. page. html Self-organization http: //www. cis. hut. fi/research/ A review on clustering http: //www. cse. msu. edu/cgi-user/web/tech/document? ID=450 Intelligent Numerical Computation 2

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Features of clustering techiques Intelligent Numerical Computation 8

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Kohonen self-organizing Algorithm Winner Updating Intelligent Numerical Computation 26

Kohonen SOM algorithm in the Euclidean space Intelligent Numerical Computation 27

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Neighborhood function Intelligent Numerical Computation 29

Simulation: square array Intelligent Numerical Computation 30

Simulation- linear array Intelligent Numerical Computation 31

Topology preservation Self-organization map of the data matrix Minimal spanning tree of the data matrix Intelligent Numerical Computation 32

Dot-product SOM Intelligent Numerical Computation 33

Learning vector quantization(LVQ) Intelligent Numerical Computation 34

Elastic Net Intelligent Numerical Computation 35

Elastic net algorithm Intelligent Numerical Computation 36

Self-organization using Potts models Math Programming Intelligent Numerical Computation 37

Self-organization using Potts models Energy function Intelligent Numerical Computation 38

Free energy and mean field equations Intelligent Numerical Computation 39

Updating rule Intelligent Numerical Computation 40

Natural elastic nets using Potts models Ø Mixed integer and linear programming Ø The learning method Ø Numerical results Intelligent Numerical Computation 41

A generative model Intelligent Numerical Computation 42

Multivariate Gaussian Intelligent Numerical Computation 43

Potts encoding Intelligent Numerical Computation 44

Log likelihood Intelligent Numerical Computation 45

Fitting a generative model Intelligent Numerical Computation 46

MILP Intelligent Numerical Computation 47

Mean field equations Intelligent Numerical Computation 48

Updating rules Intelligent Numerical Computation 49

Updating rules Intelligent Numerical Computation 50

Numerical procedure Intelligent Numerical Computation 51

Numerical results Intelligent Numerical Computation 52

Natural images Intelligent Numerical Computation 53

Local means Intelligent Numerical Computation 54