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| Presentation | 2023-03-15 11:25 Study on the Importance of Each Eigenvalue and Eigenvector for Laplacian Matrix Using Matrix Approximation Eriko Segawa, Yusuke Sakumoto (Kwansei Gakuin Univ.)  CQ2022-84 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | It is important for developing sophisticated graph algorithms to understand deeply the characteristics of the typical matrices~(e.g., Laplacian matrix and normalized Laplacian matrix) which represent the network structure. The discussion of the low-rank approximation conducts that the large eigenvalues and eigenvectors of a matrix contain more information than the small ones. Therefore, many graph algorithms use the large eigenvalues and eigenvectors. On the other hand, we clarified that the performance of anomaly detection techniques can be improved by using the combination of the large eigenvalues and the small eigenvalues. This suggests that there are cases in which the small eigenvalues and eigenvectors are also useful. However, to our best knowledge, it has not been fully understood when and why each of the eigenvalues and eigenvectors of the matrix which represents the network structure is useful. In this paper, we investigate the importance of the eigenvalues and eigenvectors for the Laplacian matrix and the normalized Laplacian matrix based on matrix approximation. We first construct the matrix approximation by easing the rank restriction in the low-rank approximation. Through the numerical examples using the constructed matrix approximation, we show that when eigenvalues and eigenvectors are useful, they exist far from the neighboring eigenvalues. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | Spectral Graph Theory / Low-Rank Approximation / Laplacian Matrix / Normalized Laplacian Matrix / Eigenvalue / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 122, no. 438, CQ2022-84, pp. 25-30, March 2023. | |
| Paper # | CQ2022-84 | |
| Date of Issue | 2023-03-08 (CQ) | |
| ISSN | Online edition: ISSN 2432-6380 | |
| Copyright and 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 | CQ2022-84 |
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| Conference Information | |
| Committee | IMQ IE MVE CQ |
| Conference Date | 2023-03-15 - 2023-03-17 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Okinawaken Seinenkaikan (Naha-shi) |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | Media of five senses, Multimedia, Media experience, Picture codinge, Image media quality, Network,quality and reliability, etc（AC） |
| Paper Information | |
| Registration To | CQ |
| Conference Code | 2023-03-IMQ-IE-MVE-CQ |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Study on the Importance of Each Eigenvalue and Eigenvector for Laplacian Matrix Using Matrix Approximation |
| Sub Title (in English) | |
| Keyword(1) | Spectral Graph Theory |
| Keyword(2) | Low-Rank Approximation |
| Keyword(3) | Laplacian Matrix |
| Keyword(4) | Normalized Laplacian Matrix |
| Keyword(5) | Eigenvalue |
| Keyword(6) | |
| Keyword(7) | |
| Keyword(8) | |
| 1st Author's Name | Eriko Segawa |
| 1st Author's Affiliation | Kwansei Gakuin University (Kwansei Gakuin Univ.) |
| 2nd Author's Name | Yusuke Sakumoto |
| 2nd Author's Affiliation | Kwansei Gakuin University (Kwansei Gakuin Univ.) |
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| Speaker | Author-1 |
| Date Time | 2023-03-15 11:25:00 |
| Presentation Time | 25 minutes |
| Registration for | CQ |
| Paper # | CQ2022-84 |
| Volume (vol) | vol.122 |
| Number (no) | no.438 |
| Page | pp.25-30 |
| #Pages | 6 |
| Date of Issue | 2023-03-08 (CQ) |
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