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Paper Abstract and Keywords
Presentation 2022-08-26 15:33
Locally-Structured Unitary Network to Capture Tangent Spaces of Manifold
Godage Yasas, Shogo Muramatsu (Niigata Univ.) SIP2022-75
Abstract (in Japanese) (See Japanese page) 
(in English) This work proposes a unique linear transform, locally-structured unitary network (LSUN), that captures tangent spaces of a manifold latent in data, enabling systematic and highly interpretable data-driven dimensionality reduction. LSUN introduces shift variability to the system with locally and adaptively controllable linear layer under the structural constraint of global unitarity. It provides shift variability that convolution does not, with the same overlap and locality as convolution. The proposed method can be an alternative method for realizing manifold learning. Existing filter-bank based transforms lack the shift-variability because they use fixed filter kernels in a convolutional structure. Local selection of filter kernels, such as sparse modeling, can capture tangent spaces, but the filter kernels obtained through training are redundant and the filters themselves are not very interpretable. To solve these problems, we propose a method to locally control coordinate axes by combining linear transforms such as rotation, shift, and butterfly layers that preserve unitarity, inspired by the multilayer structure of the non-separable oversampled
lapped transform (NSOLT). The significance of the proposed LSUN is verified through low-dimensional approximation and noise reduction experiments. As well, it is also shown that LSUN can be an approach for capturing tangent spaces.
Keyword (in Japanese) (See Japanese page) 
(in English) Tangent space learning / shift variability / unitarity / linear transforms / self-supervised learning / / /  
Reference Info. IEICE Tech. Rep., vol. 122, no. 165, SIP2022-75, pp. 129-133, Aug. 2022.
Paper # SIP2022-75 
Date of Issue 2022-08-18 (SIP) 
ISSN 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 SIP2022-75

Conference Information
Committee SIP  
Conference Date 2022-08-25 - 2022-08-26 
Place (in Japanese) (See Japanese page) 
Place (in English) Nobumoto Ohama Memorial Hall (Ishigaki Island) 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Signal processing, etc. 
Paper Information
Registration To SIP 
Conference Code 2022-08-SIP 
Language English 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Locally-Structured Unitary Network to Capture Tangent Spaces of Manifold 
Sub Title (in English)  
Keyword(1) Tangent space learning  
Keyword(2) shift variability  
Keyword(3) unitarity  
Keyword(4) linear transforms  
Keyword(5) self-supervised learning  
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1st Author's Name Godage Yasas  
1st Author's Affiliation Niigata University (Niigata Univ.)
2nd Author's Name Shogo Muramatsu  
2nd Author's Affiliation Niigata University (Niigata Univ.)
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Speaker Author-1 
Date Time 2022-08-26 15:33:00 
Presentation Time 18 minutes 
Registration for SIP 
Paper # SIP2022-75 
Volume (vol) vol.122 
Number (no) no.165 
Page pp.129-133 
#Pages 5 
Date of Issue 2022-08-18 (SIP) 

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