| Presentation | 2016-03-18 Block-sparse Extensions of Recovery Conditions of Overcomplete Dictionaries Yasushi Terazono, Kenji Yamanishi, |
|---|---|
| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | In overcomplete dictionary learning problems, observed data are modeled as products of overcomplete dictionaries and sparse signal sources, and both dictionaries and sources are estimated from data. Recent researches have shown that given a set of sufficient conditions, it is possible to obtain approximations of dictionaries with a certain error bound with a certain probability. In this paper, we extend a part of reconstruction theorems shown by Agarwal et al. to the case of block-sparse modeling, as an initial step of constructing an exact recovery theory for block-sparse cases. Agarwal et al. used inner product of data samples to quantify the degree of similarity between samples; however, under block-sparse context, an inner product of a pair of data samples does not properly evaluate the degree of similarity in the case of block-sparse. We extended or modified the assumptions on dictionary, signal sources, similarity measure so that sample similarity and commonality of non-zero blocks are properly associated under block-sparse context. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | dictionary learning / overcomplete / block-sparse |
| Paper # | IBISML2015-101 |
| Date of Issue | 2016-03-10 (IBISML) |
| Conference Information | |
| Committee | IBISML |
|---|---|
| Conference Date | 2016/3/17(2days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Institute of Statistical Mathematics |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | Statistical Mathematics, Machine Learning, Data Mining, etc. |
| Chair | Takashi Washio(Osaka Univ.) |
| Vice Chair | Kenji Fukumizu(ISM) / Masashi Sugiyama(Tokyo Inst. of Tech.) |
| Secretary | Kenji Fukumizu(ISM) / Masashi Sugiyama(Kyoto Univ.) |
| Assistant | Koji Tsuda(Univ. of Tokyo) / Hisashi Kashima(Kyoto Univ.) |
| Paper Information | |
| Registration To | Technical Committee on Infomation-Based Induction Sciences and Machine Learning |
|---|---|
| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Block-sparse Extensions of Recovery Conditions of Overcomplete Dictionaries |
| Sub Title (in English) | |
| Keyword(1) | dictionary learning |
| Keyword(2) | overcomplete |
| Keyword(3) | block-sparse |
| 1st Author's Name | Yasushi Terazono |
| 1st Author's Affiliation | The University of Tokyo(UTokyo) |
| 2nd Author's Name | Kenji Yamanishi |
| 2nd Author's Affiliation | The University of Tokyo(UTokyo) |
| Date | 2016-03-18 |
| Paper # | IBISML2015-101 |
| Volume (vol) | vol.115 |
| Number (no) | IBISML-511 |
| Page | pp.pp.55-58(IBISML), |
| #Pages | 4 |
| Date of Issue | 2016-03-10 (IBISML) |