| Presentation | 2017-03-20 Structure Estimation of Topological Manifolds and Manifold Learning Hajime Tasaki, Reiner Lenz, Jinhui Chao, |
|---|---|
| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | Manifold learning algorithms try to find the low dimensional representation of high dimensional data for the visualization or the reduction of redundency and computational complexity. It is usually assumed that data cloud has a structure of low dimensional submanifold in high dimensional space. However it seems that most manifold learning algorithms lack clear and rigor treatment if not confuse different structures of a manifold. E.g. no procedure contained to catch the topological structure of manifolds. In this research, we propose a novel framework for manifold learning. The proposed method contains a procedure to determine the structure of topological manifold starting from to build a system of neighborhoods and determine local dimension in order to separate data cloud as a simplicial complex to components of manifolds with different dimensions. After construction of chart maps for each manifolds, global topology such as holes or loops can be found using topological invariants. In particular, we show the necessity to distinguish between different dimensions of manifolds e.g. local or intrinsic dimension and global or extrinsic dimensions. Robust algorithms are shown to estimate these dimensions using topological stability in scale space. We show how to use all sizes of neighborhoods to find local and global dimension. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Manifold Learning / Topology / Simplicial Complex / Dimension Estimation |
| Paper # | BioX2016-35,PRMU2016-198 |
| Date of Issue | 2017-03-13 (BioX, PRMU) |
| Conference Information | |
| Committee | PRMU / BioX |
|---|---|
| Conference Date | 2017/3/20(2days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Chair | Eisaku Maeda(NTT) / Masakatsu Nishigaki(Shizuoka Univ.) |
| Vice Chair | Seiichi Uchida(Kyushu Univ.) / Hironobu Fujiyoshi(Chubu Univ.) / Akira Otsuka(AIST) / Hiroshi Takano(Toyama Pref. Univ.) |
| Secretary | Seiichi Uchida(Kyoto Univ.) / Hironobu Fujiyoshi(NTT) / Akira Otsuka(NEC) / Hiroshi Takano(AIST) |
| Assistant | Masaki Oonishi(AIST) / Takuya Funatomi(NAIST) / Masatsugu Ichino(Univ. of Electro-Comm.) / Naoyuki Takada(Secom) / Takahiro Aoki(Fujitsu Labs.) |
| Paper Information | |
| Registration To | Technical Committee on Pattern Recognition and Media Understanding / Technical Committee on Biometrics |
|---|---|
| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Structure Estimation of Topological Manifolds and Manifold Learning |
| Sub Title (in English) | |
| Keyword(1) | Manifold Learning |
| Keyword(2) | Topology |
| Keyword(3) | Simplicial Complex |
| Keyword(4) | Dimension Estimation |
| 1st Author's Name | Hajime Tasaki |
| 1st Author's Affiliation | Chuo University(Chuo Univ.) |
| 2nd Author's Name | Reiner Lenz |
| 2nd Author's Affiliation | Linkoping University(Linkoping Univ.) |
| 3rd Author's Name | Jinhui Chao |
| 3rd Author's Affiliation | Chuo University(Chuo Univ.) |
| Date | 2017-03-20 |
| Paper # | BioX2016-35,PRMU2016-198 |
| Volume (vol) | vol.116 |
| Number (no) | BioX-527,PRMU-528 |
| Page | pp.pp.11-15(BioX), pp.11-15(PRMU), |
| #Pages | 5 |
| Date of Issue | 2017-03-13 (BioX, PRMU) |