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Paper Abstract and Keywords
Presentation 2017-03-20 10:50
Structure Estimation of Topological Manifolds and Manifold Learning
Hajime Tasaki (Chuo Univ.), Reiner Lenz (Linkoping Univ.), Jinhui Chao (Chuo Univ.) BioX2016-35 PRMU2016-198
Abstract (in Japanese) (See Japanese page) 
(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) 
(in English) Manifold Learning / Topology / Simplicial Complex / Dimension Estimation / / / /  
Reference Info. IEICE Tech. Rep., vol. 116, no. 528, PRMU2016-198, pp. 11-15, March 2017.
Paper # PRMU2016-198 
Date of Issue 2017-03-13 (BioX, PRMU) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
Copyright
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reproduction		 All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
Download PDF BioX2016-35 PRMU2016-198

Conference Information
Committee PRMU BioX  
Conference Date 2017-03-20 - 2017-03-21 
Place (in Japanese) (See Japanese page) 
Place (in English)  
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To PRMU 
Conference Code 2017-03-PRMU-BioX 
Language Japanese 
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  
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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.)
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Speaker Author-1 
Date Time 2017-03-20 10:50:00 
Presentation Time 25 minutes 
Registration for PRMU 
Paper # BioX2016-35, PRMU2016-198 
Volume (vol) vol.116 
Number (no) no.527(BioX), no.528(PRMU) 
Page pp.11-15 
#Pages 5 
Date of Issue 2017-03-13 (BioX, PRMU) 

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