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)

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

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

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

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

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

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

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

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

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= k=98

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

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

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