1. Intelligent Database Systems Lab 國立雲林科技大學 National Yunlin University of Science and Technology 1 Exploiting Data Topology in Visualization and Clustering of Self-Organizing Maps Kadim Tas ¸demir and Erzsébet Merényi, Senior Member TNN, 2011 Presented by Hung-Yi Cai 2011/3/9

2. Intelligent Database Systems Lab N.Y.U.S.T. I. M. 2 Outlines  Motivation  Objectives  Previous Study  Methodology  Experiments  Conclusions  Comments

3. Intelligent Database Systems Lab N.Y.U.S.T. I. M. 3 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.

4. Intelligent Database Systems Lab N.Y.U.S.T. I. M. 4 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.

5. Intelligent Database Systems Lab N.Y.U.S.T. 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. 5

6. Intelligent Database Systems Lab N.Y.U.S.T. I. M. Methodology Topology visualization through connectivity matrix of SOM prototypes CONNvis: visualization of the connectivity matrix Assessment of topology preservation with CONNvis 6

7. Intelligent Database Systems Lab N.Y.U.S.T. 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, RF ij means w i is the BMU and w j is the second BMU. 7

8. Intelligent Database Systems Lab N.Y.U.S.T. 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 w i. ─ Reveals most-to-least dense regions local to w i in data space. 8

9. Intelligent Database Systems Lab N.Y.U.S.T. I. M. The threshold of width 9

10. Intelligent Database Systems Lab 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). 10

11. Intelligent Database Systems Lab N.Y.U.S.T. I. M. Remove weak connections  Remove weak connections that link any two coarse clusters X and Y at their boundary 11

12. Intelligent Database Systems Lab N.Y.U.S.T. I. M. Experiments  A real remote sensing spectral image of Ocean City 12

13. Intelligent Database Systems Lab N.Y.U.S.T. I. M. Experiments  Compare to U-matrix and ISOMAP 13

14. Intelligent Database Systems Lab N.Y.U.S.T. I. M. 14 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.

15. Intelligent Database Systems Lab N.Y.U.S.T. I. M. 15 Comments  Advantages ─ CONNvis greatly assists in detailed identification of cluster boundaries.  Applications ─ Data Clustering