| Presentation | 2023-03-15 Study on the Importance of Each Eigenvalue and Eigenvector for Laplacian Matrix Eriko Segawa, Yusuke Sakumoto, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(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 thispaper, 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 eigenvectorsare useful, they exist far from the neighboring eigenvalues. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Spectral Graph Theory / Low-Rank Approximation / Laplacian Matrix / Normalized Laplacian Matrix / Eigenvalue |
| Paper # | CQ2022-84 |
| Date of Issue | 2023-03-08 (CQ) |
| Conference Information | |
| Committee | IMQ / IE / MVE / CQ |
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| Conference Date | 2023/3/15(3days) |
| 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） |
| Chair | Kenya Uomori(Osaka Univ.) / Kazuya Kodama(NII) / Kiyoshi Kiyokawa(NAIST) / Jun Okamoto(NTT) |
| Vice Chair | Mitsuru Maeda(Canon) / Hiroyuki Bandoh(NTT) / Toshihiko Yamazaki(Univ. of Tokyo) / Sumaru Niida(KDDI Research) / Takefumi Hiraguri(Nippon Inst. of Tech.) / Gou Hasegawa(Tohoku Univ.) |
| Secretary | Mitsuru Maeda(Nagoya Univ.) / Hiroyuki Bandoh(NTT) / Toshihiko Yamazaki(KDDI Research) / Sumaru Niida(Nagoya Inst. of Tech.) / Takefumi Hiraguri(NAIST) / Gou Hasegawa(DNP) |
| Assistant | Masato Tsukada(Univ. of Tsukuba) / Takashi Yamazoe(Seikei Univ.) / Shunsuke Iwamura(NHK) / Shinobu Kudo(NTT) / Hidehiko Shishido(Univ. of Tsukuba) / Atsushi Nakazawa(Kyoto Univ.) / Naoya Tojo(KDDI Research) / Naoki Hagiyama(NTT) / Kimiko Kawashima(NTT) / Ryo Nakamura(Fukuoka Univ.) / Toshiro Nakahira(NTT) / Kenta Tsukatsune(Okayama Univ. of Science) |
| Paper Information | |
| Registration To | Technical Committee on Image Media Quality / Technical Committee on Image Engineering / Technical Committee on Media Experience and Virtual Environment / Technical Committee on Communication Quality |
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| Language | JPN |
| 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 |
| 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 |
| 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.) |
| Date | 2023-03-15 |
| Paper # | CQ2022-84 |
| Volume (vol) | vol.122 |
| Number (no) | CQ-438 |
| Page | pp.pp.25-30(CQ), |
| #Pages | 6 |
| Date of Issue | 2023-03-08 (CQ) |