| Item type |
SIG Technical Reports(1) |
| 公開日 |
2020-01-22 |
| タイトル |
|
|
タイトル |
Online Row Sampling from Random Streams |
| タイトル |
|
|
言語 |
en |
|
タイトル |
Online Row Sampling from Random Streams |
| 言語 |
|
|
言語 |
eng |
| 資源タイプ |
|
|
資源タイプ識別子 |
http://purl.org/coar/resource_type/c_18gh |
|
資源タイプ |
technical report |
| 著者所属 |
|
|
|
The University of Tokyo |
| 著者所属 |
|
|
|
Keio University |
| 著者所属(英) |
|
|
|
en |
|
|
The University of Tokyo |
| 著者所属(英) |
|
|
|
en |
|
|
Keio University |
| 著者名 |
Masataka, Gohda
Naonori, Kakimura
|
| 著者名(英) |
Masataka, Gohda
Naonori, Kakimura
|
| 論文抄録 |
|
|
内容記述タイプ |
Other |
|
内容記述 |
This paper studies spectral approximation for a positive semidefinite matrix in the online setting. It is known in [Cohen et al. APPROX 2016] that we can construct a spectral approximation of a given n × d matrix in the online setting if an additive error is allowed. In this paper, we propose an online algorithm that avoids an additive error with the same time and space complexities as the algorithm of Cohen et al., and provides a better upper bound on the approximation size when a given matrix has small rank. In addition, we consider the online random order setting where a row of a given matrix arrives uniformly at random. In this setting, we propose time and space efficient algorithms to find a spectral approximation. Moreover, we reveal that a lower bound on the approximation size in the online random order setting is Ω(dε-2 log n), which is larger than the one in the offline setting by an O (log n) factor. |
| 論文抄録(英) |
|
|
内容記述タイプ |
Other |
|
内容記述 |
This paper studies spectral approximation for a positive semidefinite matrix in the online setting. It is known in [Cohen et al. APPROX 2016] that we can construct a spectral approximation of a given n × d matrix in the online setting if an additive error is allowed. In this paper, we propose an online algorithm that avoids an additive error with the same time and space complexities as the algorithm of Cohen et al., and provides a better upper bound on the approximation size when a given matrix has small rank. In addition, we consider the online random order setting where a row of a given matrix arrives uniformly at random. In this setting, we propose time and space efficient algorithms to find a spectral approximation. Moreover, we reveal that a lower bound on the approximation size in the online random order setting is Ω(dε-2 log n), which is larger than the one in the offline setting by an O (log n) factor. |
| 書誌レコードID |
|
|
収録物識別子タイプ |
NCID |
|
収録物識別子 |
AN1009593X |
| 書誌情報 |
研究報告アルゴリズム（AL）
巻 2020-AL-176,
号 2,
p. 1-8,
発行日 2020-01-22
|
| ISSN |
|
|
収録物識別子タイプ |
ISSN |
|
収録物識別子 |
2188-8566 |
| Notice |
|
|
|
SIG Technical Reports are nonrefereed and hence may later appear in any journals, conferences, symposia, etc. |
| 出版者 |
|
|
言語 |
ja |
|
出版者 |
情報処理学会 |
IPSJ-AL20176002.pdf (749.3 kB)
