|
Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Information Science and Technology / Faculty of Information Science and Technology >
Peer-reviewed Journal Articles, etc >
A column-wise update algorithm for nonnegative matrix factorization in Bregman divergence with an orthogonal constraint
| Title: | A column-wise update algorithm for nonnegative matrix factorization in Bregman divergence with an orthogonal constraint |
| Authors: | Kimura, Keigo Browse this author | | Kudo, Mineichi Browse this author →KAKEN DB | | Tanaka, Yuzuru Browse this author |
| Keywords: | Orthogonal nonnegative matrix factorization | | Orthogonal Factorization | | Bregman Divergence | | Column-wise Update |
| Issue Date: | May-2016 |
| Publisher: | Springer |
| Journal Title: | Machine learning |
| Volume: | 103 |
| Issue: | 2 |
| Start Page: | 285 |
| End Page: | 306 |
| Publisher DOI: | 10.1007/s10994-016-5553-0 |
| Abstract: | Recently orthogonal nonnegative matrix factorization (ONMF), imposing an orthogonal constraint into NMF, has been attracting a great deal of attention. ONMF is more appropriate than standard NMF for a clustering task because the constrained matrix can be considered as an indicator matrix. Several iterative ONMF algorithms have been proposed, but they suffer from slow convergence because of their matrix-wise updating. In this paper, therefore, a column-wise update algorithm is proposed for speeding up ONMF. To make the idea possible, we transform the matrix-based orthogonal constraint into a set of column-wise orthogonal constraints. The algorithm is stated first with the Frobenius norm and then with Bregman divergence, both for measuring the degree of approximation. Experiments on one artificial and six real-life datasets showed that the proposed algorithms converge faster than the other conventional ONMF algorithms, more than four times in the best cases, due to their smaller numbers of iterations. |
| Rights: | The final publication is available at Springer via http://dx.doi.org/10.1007/s10994-016-5553-0 |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/65181 |
| Appears in Collections: | 情報科学院・情報科学研究院 (Graduate School of Information Science and Technology / Faculty of Information Science and Technology) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
|
Submitter: 木村 圭吾
|
