exploiting data topology in visualization and clustering of self-organizing maps

Intelligent Database Systems Lab

國立雲林科技大學National Yunlin University of Science and Technology

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Exploiting Data Topology in Visualization and Clustering of Self-Organizing Maps

Kadim Tas ¸demir and Erzsébet Merényi, Senior MemberTNN, 2011

Presented by Hung-Yi Cai2011/3/9


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Outlines· Motivation· Objectives· Previous Study· Methodology· Experiments· Conclusions· Comments


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Motivation

· Different aspects of the information learned by the SOM are presented by existing methods, but data topology, which is present in the SOM’s knowledge, is greatly underutilized.

· Data topology can be integrated into the visualization of the SOM and thereby provide a more elaborate view of the cluster structure than existing schemes.


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Objectives

· To integrate the data topology, present in the SOM’s knowledge, into the visualization of the SOM for improved capture of clusters.

· This objective will be accomplished through a new concept of the “connectivity matrix” and its specific rendering over the SOM.


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I. M.Previous Study· SOM is a topology preserving mapping

─ Ideally, prototypes(neurons) those are neighbors in SOM map are also neighbors (centroids of neighboring Voronoi polyhedra) in data space and vice versa.

· Growing SOM ─ It appears less robust than the Kohonen SOM because of the large

number of parameters needing adjustment.

· ViSOM─ it requires a relatively large number of prototypes even for small data

sets.

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I. M.Methodology Topology visualization through connectivity matrix of SOM

prototypes CONNvis: visualization of the connectivity matrix Assessment of topology preservation with CONNvis

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I. M.Topology visualization through connectivity matrix of SOM prototypes

· Induced Delaunay Triangulation and Voronoi─ It can be determined from the relationships of the best

matching units (BMUs) and the second BMUs.

· Connectivity Matrix─ It is a weighted analog of A, where the weights indicate the

density distribution of the input data among the prototypes adjacent in M.

─ where, RFij means wi is the BMU and wj is the second BMU.

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N

j iji RFRF1jiij RFRFjiCONN ),(


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I. M.CONNvis: visualization of the connectivity matrix

· Line width： Global Importance─ The strength of the connection and reflects the density

distribution among the connected units.

· Line colors： Local Importance─ A ranking of the connectivity strengths of wi .

─ Reveals most-to-least dense regions local to wi in data space.

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N.Y.U.S.T.

I. M.Assessment of topology preservation with CONNvis

· Topology violations─ connected neural units that are not immediate

neighbors in map (forward topology violations); ─ unconnected neural units that are immediate neighbors

in map (backward topology violations).

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I. M.Remove weak connections

· Remove weak connections that link any two coarse clusters X and Y at their boundary

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· A real remote sensing spectral image of Ocean City

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· Compare to U-matrix and ISOMAP

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Conclusions· CONNvis integrates data distribution into the

customary Delaunay triangulation, which, when displayed on the SOM grid, enables 2-D visualization of the manifold structure regardless of the data dimensionality.

· CONNvis is also unique among SOM representations in that it shows both forward and backward topology violations on the SOM grid.


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Comments

· Advantages─ CONNvis greatly assists in detailed identification of

cluster boundaries.

· Applications─ Data Clustering

exploiting data topology in visualization and clustering of self-organizing maps

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