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| Presentation | 2019-12-13 13:00 [Invited Talk] Spectral Sparsification of Hypergraphs Tasuku Soma (The Univ. of Tokyo), Yuichi Yoshida (NII)  COMP2019-35 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | For an undirected/directed hypergraph G = (V, E), its Laplacian LG : ℝv → ℝv is defined such that its “quadratic form” x⊺LG (x) captures the cut information of G. In particular, 1S⊺LG(1S) coincides with the cut size of S ⊆ V, where 1S ∊ ℝV is the characteristic vector of S. A weighted subgraph H of a hypergraph G on a vertex set V is said to be an ∊-spectral sparsifier of G if (1 – ∊)x⊺ LH(x) ≤ x⊺ LG(x) ≤ (1 + ∊)x⊺ LH(x) holds for every x ∊ ℝV. In this paper, we present a polynomial-time algorithm that, given an undirected/directed hypergraph G on n vertices, constructs an ∊-spectral sparsifier of G with O(n3 log n/∊2) hyperedges/hyperarcs. The proposed spectral sparsification can be used to improve the time and space complexities of algorithms for solving problems that involve the quadratic form, such as computing the eigenvalues of LG, computing the effective resistance between a pair of vertices in G, semi-supervised learning based on LG, and cut problems on G. In addition, our sparsification result implies that any nonnegative hypernetwork type submodular function can be concisely represented by a directed hypergraph of polynomial size, even if the original representation is of exponential size. Accordingly, we show that, for any distribution, we can properly and agnostically learn nonnegative hypernetwork type submodular functions with O(n4 log(n/∊)/∊4) samples. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | Spectral sparsification / Hypergraph / Learning theory / / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 119, no. 340, COMP2019-35, pp. 45-45, Dec. 2019. | |
| Paper # | COMP2019-35 | |
| Date of Issue | 2019-12-06 (COMP) | |
| 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 | COMP2019-35 |
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| Conference Information | |
| Committee | COMP |
| Conference Date | 2019-12-13 - 2019-12-13 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Ikaho Seminar House, Gunma University |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | COMP |
| Conference Code | 2019-12-COMP |
| Language | English |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Spectral Sparsification of Hypergraphs |
| Sub Title (in English) | |
| Keyword(1) | Spectral sparsification |
| Keyword(2) | Hypergraph |
| Keyword(3) | Learning theory |
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| 1st Author's Name | Tasuku Soma |
| 1st Author's Affiliation | The University of Tokyo (The Univ. of Tokyo) |
| 2nd Author's Name | Yuichi Yoshida |
| 2nd Author's Affiliation | National Institute of Informatics (NII) |
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| Speaker | Author-1 |
| Date Time | 2019-12-13 13:00:00 |
| Presentation Time | 60 minutes |
| Registration for | COMP |
| Paper # | COMP2019-35 |
| Volume (vol) | vol.119 |
| Number (no) | no.340 |
| Page | p.45 |
| #Pages | 1 |
| Date of Issue | 2019-12-06 (COMP) |
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