1. Intelligent Database Systems Lab 國立雲林科技大學 National Yunlin University of Science and Technology Topology Preservation in Self-Organizing Feature Maps: Exact Definition and Measurement Presenter : Zhen-Feng Weng Authors : Thomas Villmann, Ralf Der, Michael Herrmann, and Thomas M. Martinetz 2009/12/15 TNN.11 (1997)

2. N.Y.U.S.T. I. M. Intelligent Database Systems Lab 2 Outline Introduction Motivation Objective Method Experiments Conclusion Comments

3. N.Y.U.S.T. I. M. Intelligent Database Systems Lab 3 Introduction Every dataset which has own manifold is suitable to different lattice structure.  What kind structure is good? To measure Topology Preservation. Definition of topology preservation The projected map A B C ABC

4. N.Y.U.S.T. I. M. Intelligent Database Systems Lab 4 Motivation All approaches are based on the evaluations of the position of the neurons in lattice.  To take the form of the data manifold into the measurement

5. N.Y.U.S.T. I. M. Intelligent Database Systems Lab 5 Motivation (cont.) Topology Preservation Cannot only consider Euclidean distance A B C ABC

6. N.Y.U.S.T. I. M. Intelligent Database Systems Lab 6 Objective It proposed a new approach for quantifying topology preservation which can take structure of data manifold into account. A B C ABC

7. N.Y.U.S.T. I. M. Intelligent Database Systems Lab 7 Topographic function Divide the function into two parts:  M->A neighborhood preservation Distance measure  A->M neighborhood preservation Euclidean measure, the weight of neurons Neighborhood dist is 1

8. N.Y.U.S.T. I. M. Intelligent Database Systems Lab 8 Topographic function (cont.) Only the maximum dist is not enough  Add Delaunay Triangulation (D M ) receptive field Use connectivity matrix C to calculate D M

9. N.Y.U.S.T. I. M. Intelligent Database Systems Lab 9 Example of topographic function

10. N.Y.U.S.T. I. M. Intelligent Database Systems Lab 10 Comparison with topographic product topographic product is the most popular in topology preservation measure dM,dA is Euclidean distance P=-0.107 k=98

11. N.Y.U.S.T. I. M. Intelligent Database Systems Lab 11 Experiments 1-d 2-d 3-d Input space: 6-D Output space: 3-D The less, the better 4-d 3-d 2-d Best dim is 2.34

12. N.Y.U.S.T. I. M. Intelligent Database Systems Lab 12 Conclusions It presented a novel approach to measure topology preservation of a SOFM.  Consider the input manifold  More suitable to calculate distance

13. N.Y.U.S.T. I. M. Intelligent Database Systems Lab 13 Comments Advantage  Theoretical, improve our background Drawback  Lack figures to explain Application  How to improve classification