1. TreeSOM :Cluster analysis in the self- organizing map Neural Networks 19 (2006) 935-949 2006 Special Issue Reporter 張欽隆 D9515012

2. What is SOM Self-Organizing Map(Kohonen, 1987) Mapping high-dimensional data onto a low-dimensional grid Similar data elements are placed close together

3. SOM A SOM consists of neurons organized on a regular low dimensional grid Each neuron has a weight vector During training, neighboring neurons on the grid get similar weight vector. (come closer) Finally, similar data elements are placed close together.

4. Problem of SOM Different map initializations and input order of data elements may result in different clustering. For large data sets, analyze different clustering for finding best clustering is a lengthy and laborious task

5. This paper present… A new SOM visualization An unsupervised method for cluster analysis and confidence testing for finding reliable clustering.

6. Outline Visualization Cluster discovery Calibration Best clustering SOM as Tree Cluster confidence The most representative SOM

7. Visualization Tree variants of SOM visualization with umat (u-matrix, kraaijveld, Mao & Jain, 1992) –(a) each cell is shaded according to the average distance form the neuron to its neighbors. –(b) Grid density is double, some cells represent neurons and other are borders. –(c) Use original SOM grid density but draw the borders between the neurons as thick lines Base on representation (c),we can define a cluster as a group of nodes surrounded by an uninterrupted border of a given shade.

8. Cluster discovery Cluster: a group of nodes with short distances between them and long distances to the other nodes. Algorithm for finding cluster: each node within a cluster must be connected to at least one other node within the same cluster with an edge that is shorter than the distance threshold.

9. Cluster discovery: clustering map Cluster borders are always displayed in black Cluster area are shaded according to the average distance between the nodes within the cluster. (nodes density)

10. Calibration Mapping data on a trained SOM is called calibration. The clusters are shaded according to the average distance between the data elements. (element density)

11. Best clustering Problem: –Data is grouped into few large loose cluster at high thresholds  the clustering may be too coarse, grouping together unrelated items. –Data is grouped into many small tighter clusters at low thresholds  the clustering may be too fine, unnecessarily separating similar items. What is best clustering ? –The clustering with the tightest clusters with the greatest distances between them.( looseness / average distance ) –Algorithm:

12. SOM as Tree Why Tree ? –Traditional hierarchical clusterings visualization use tree. –Comparison become easier if the SOM itself is represented as a tree.

13. Cluster confidence Problem: SOM (clustering) may be different with different initialization and input order. How to determine the “true” clustering ? –Only the clusters found in the majority of cases, may be included in the final clustering (Kohonen) Consensus tree was used to tackle this problem.(Margush and McMorris, 1981)

14. Conensus tree – node equivalence Node equivalence –Two nodes are equivalent if their sets of leaves are identical.

15. Consensus tree Confidence value Base on confidence values, the consensus tree is built, starting with the nodes with confidence above 50%.

16. The most representative SOM The most representative SOM is the one which is closest to the consensus tree. How to measure the similarity ? –The more nodes are equivalent between two tree, the more similar they are.