國立雲林科技大學 National Yunlin University of Science and Technology Self-organizing map learning nonlinearly embedded manifoldsmanifolds Author :Timo Simila Reporter : Tse Ho Lin 2007/11/21 1 Information Visualization, 2002

N.Y.U.S.T. I. M. Outline Motivation Objectives Methodology Experiments Conclusion Personal Comments 2

N.Y.U.S.T. I. M. Motivation The problem of nonlinearly embedded manifolds of SOM 3 Training

N.Y.U.S.T. I. M. Objectives We propose a modification of the Self- organizing map (SOM) algorithm that is able to learn the manifold structure in the high- dimensional observation coordinates. 4 Training

N.Y.U.S.T. I. M. Methodology 5 LLE SOM

N.Y.U.S.T. I. M. Methodology 6

N.Y.U.S.T. I. M. Experiments 7

N.Y.U.S.T. I. M. Experiments 8

N.Y.U.S.T. I. M. Experiments 9

N.Y.U.S.T. I. M. Conclusion The proposed algorithm is able to learn nonlinearly embedded manifolds. 10

N.Y.U.S.T. I. M. Personal Comments Application  High-dimensional data sets with nonlinearly embedded manifolds. Advantage  … Drawback  The M-SOM is limited to the cases in which the data forms a manifold structure. 11

N.Y.U.S.T. I. M. Appendix: LLE 12 If X j not belong to K nearest neighbors then W ij =0 min Constraint

N.Y.U.S.T. I. M. Appendix: Manifold 13