| Presentation | 2016-01-29 Riemannian preconditioning for tensor completion Hiroyuki Kasai, Bamdev Mishra, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | We propose a novel Riemannian preconditioning approach for the tensor completion problem with rank constraint. A Riemannian metric or inner product is proposed that exploits the least-squares structure of the cost function and takes into account the structured symmetry in Tucker decomposition. The specific metric allows to use the versatile framework of Riemannian optimization on quotient manifolds to develop a preconditioned nonlinear conjugate gradient algorithm for the problem. To this end, concrete matrix representations of various optimization-related ingredients are listed. Numerical comparisons suggest that our proposed algorithm robustly outperforms state-of-the-art algorithms across different problem instances encompassing various synthetic and real-world datasets. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Riemannian optimization / Structured symmetry / Least-squares / Tailored Riemannian metric / Quotient Manifold / Tucker decomposition |
| Paper # | MoNA2015-50 |
| Date of Issue | 2016-01-21 (MoNA) |
| Conference Information | |
| Committee | MICT / ASN / MoNA |
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| Conference Date | 2016/1/28(2days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Hotel Okada |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | Ambient intelligence, ICT for Medical, Healthcare and Sports, etc |
| Chair | Ryuji Kohno(Yokohama National Univ.) / Hiroshi Tohjo(NTT) / Hiroaki Morino(Shibaura Inst. of Tech.) |
| Vice Chair | Masaru Sugimachi(National Cerebral and Cardiovascular Center) / Takahiro Aoyagi(Tokyo Inst. of Tech.) / Hiroo Sekiya(Chiba Univ.) / Hiraku Okada(Nagoya Univ.) / Kiyohito Yoshihara(KDDI R&D Labs.) / Ryoichi Shinkuma(Kyoto Univ.) |
| Secretary | Masaru Sugimachi(NICT) / Takahiro Aoyagi(Nagoya Inst. of Tech.) / Hiroo Sekiya(Kanagawa Inst. of Tech.) / Hiraku Okada(NTT) / Kiyohito Yoshihara(KDDI R&D Labs.) / Ryoichi Shinkuma(Kumamoto Univ.) |
| Assistant | Kohei Ohno(Meiji Univ.) / Keisuke Shima(Yokohama National Univ.) / Tomoko Tateyama(Ritsumeikan Univ.) / Yuichi Igarashi(Hitachi) / Katsuhiro Naito(Aichi Inst. of Tech.) / Kiyohiko Hattori(NICT) / Hiroshi Fujita(Fujitsu Labs.) / Takuro Yonezawa(Keio Univ.) / Yoshifumi Morihiro(NTT DoCoMo) / Hisashi Kurasawa(NTT) / Makoto Suzuki(Univ. of Tokyo) |
| Paper Information | |
| Registration To | Technical Committee on Healthcare and Medical Information Communication Technology / Technical Committee on Ambient intelligence and Sensor Networks / Technical Committee on Mobile Network and Applications |
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| Language | ENG |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Riemannian preconditioning for tensor completion |
| Sub Title (in English) | |
| Keyword(1) | Riemannian optimization |
| Keyword(2) | Structured symmetry |
| Keyword(3) | Least-squares |
| Keyword(4) | Tailored Riemannian metric |
| Keyword(5) | Quotient Manifold |
| Keyword(6) | Tucker decomposition |
| 1st Author's Name | Hiroyuki Kasai |
| 1st Author's Affiliation | The University of Electro-Communications(UEC) |
| 2nd Author's Name | Bamdev Mishra |
| 2nd Author's Affiliation | University of Cambridge, University of Li`ege, Amazon Development Centre India(Uni. of Cambridge, Uni. of Li`ege, Amazon Dev. Cent. India) |
| Date | 2016-01-29 |
| Paper # | MoNA2015-50 |
| Volume (vol) | vol.115 |
| Number (no) | MoNA-436 |
| Page | pp.pp.55-60(MoNA), |
| #Pages | 6 |
| Date of Issue | 2016-01-21 (MoNA) |