| Presentation | 2019-12-13 [Invited Talk] Spectral Sparsification of Hypergraphs Tasuku Soma, Yuichi Yoshida, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | For an undirected/directed hypergraph G = (V, E), its Laplacian LG : ?v → ?v 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 ? ?V 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 ? ?V. 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. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Spectral sparsificationHypergraphLearning theory |
| Paper # | COMP2019-35 |
| Date of Issue | 2019-12-06 (COMP) |
| Conference Information | |
| Committee | COMP |
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| Conference Date | 2019/12/13(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Ikaho Seminar House, Gunma University |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Chair | Toshihiro Fujito(Toyohashi Univ. of Tech.) |
| Vice Chair | Shinichi Nakano(Gunma Univ.) |
| Secretary | Shinichi Nakano(Kumamoto Univ) |
| Assistant | Kazuhisa Seto(Seikei Univ.) |
| Paper Information | |
| Registration To | Technical Committee on Theoretical Foundations of Computing |
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| Language | ENG |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | [Invited Talk] Spectral Sparsification of Hypergraphs |
| Sub Title (in English) | |
| Keyword(1) | Spectral sparsificationHypergraphLearning theory |
| 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) |
| Date | 2019-12-13 |
| Paper # | COMP2019-35 |
| Volume (vol) | vol.119 |
| Number (no) | COMP-340 |
| Page | pp.pp.45-45(COMP), |
| #Pages | 1 |
| Date of Issue | 2019-12-06 (COMP) |