Sparse nonnegative matrix factorization with ℓ(0)-constraints
Although nonnegative matrix factorization (NMF) favors a sparse and part-based representation of nonnegative data, there is no guarantee for this behavior. Several authors proposed NMF methods which enforce sparseness by constraining or penalizing the [Formula: see text] of the factor matrices. On t...
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| Vydáno v: | Neurocomputing (Amsterdam) Ročník 80; číslo 1; s. 38 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
15.03.2012
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| ISSN: | 0925-2312 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | Although nonnegative matrix factorization (NMF) favors a sparse and part-based representation of nonnegative data, there is no guarantee for this behavior. Several authors proposed NMF methods which enforce sparseness by constraining or penalizing the [Formula: see text] of the factor matrices. On the other hand, little work has been done using a more natural sparseness measure, the [Formula: see text]. In this paper, we propose a framework for approximate NMF which constrains the [Formula: see text] of the basis matrix, or the coefficient matrix, respectively. For this purpose, techniques for unconstrained NMF can be easily incorporated, such as multiplicative update rules, or the alternating nonnegative least-squares scheme. In experiments we demonstrate the benefits of our methods, which compare to, or outperform existing approaches.Although nonnegative matrix factorization (NMF) favors a sparse and part-based representation of nonnegative data, there is no guarantee for this behavior. Several authors proposed NMF methods which enforce sparseness by constraining or penalizing the [Formula: see text] of the factor matrices. On the other hand, little work has been done using a more natural sparseness measure, the [Formula: see text]. In this paper, we propose a framework for approximate NMF which constrains the [Formula: see text] of the basis matrix, or the coefficient matrix, respectively. For this purpose, techniques for unconstrained NMF can be easily incorporated, such as multiplicative update rules, or the alternating nonnegative least-squares scheme. In experiments we demonstrate the benefits of our methods, which compare to, or outperform existing approaches. |
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| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| ISSN: | 0925-2312 |
| DOI: | 10.1016/j.neucom.2011.09.024 |