Sparse nonnegative matrix factorization using ℓ0-constraints

Robert Peharz; Michael Stark; Franz Pernkopf

doi:10.1109/MLSP.2010.5589219

Sparse nonnegative matrix factorization using ℓ⁰-constraints

Robert Peharz, Michael Stark, Franz Pernkopf

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

19 Citations (Scopus)

Abstract

Although nonnegative matrix factorization (NMF) favors a part-based and sparse representation of its input, there is no guarantee for this behavior. Several extensions to NMF have been proposed in order to introduce sparseness via the ℓ¹-norm, while little work is done using the more natural sparseness measure, the ℓ⁰-pseudo-norm. In this work we propose two NMF algorithms with ℓ⁰-sparseness constraints on the bases and the coefficient matrices, respectively. We show that classic NMF [1] is a suited tool for ℓ⁰-sparse NMF algorithms, due to a property we call sparseness maintenance. We apply our algorithms to synthetic and real-world data and compare our results to sparse NMF [2] and nonnegative KSVD [3].

Original language	English
Title of host publication	Proceedings of the 2010 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2010
Publisher	Institute of Electrical and Electronics Engineers
Pages	83-88
Number of pages	6
ISBN (Print)	9781424478774
DOIs	https://doi.org/10.1109/MLSP.2010.5589219
Publication status	Published - 24 Nov 2010
Externally published	Yes
Event	20th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2010 - Kittila, Finland Duration: 29 Aug 2010 → 1 Sept 2010 Conference number: 20

Conference

Conference	20th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2010
Abbreviated title	MLSP 2010
Country/Territory	Finland
City	Kittila
Period	29/08/10 → 1/09/10

Access to Document

10.1109/MLSP.2010.5589219

Cite this

@inproceedings{c09c19a08a3b4b62b8fa763d829a17f2,

title = "Sparse nonnegative matrix factorization using ℓ0-constraints",

abstract = "Although nonnegative matrix factorization (NMF) favors a part-based and sparse representation of its input, there is no guarantee for this behavior. Several extensions to NMF have been proposed in order to introduce sparseness via the ℓ1-norm, while little work is done using the more natural sparseness measure, the ℓ0-pseudo-norm. In this work we propose two NMF algorithms with ℓ0-sparseness constraints on the bases and the coefficient matrices, respectively. We show that classic NMF [1] is a suited tool for ℓ0-sparse NMF algorithms, due to a property we call sparseness maintenance. We apply our algorithms to synthetic and real-world data and compare our results to sparse NMF [2] and nonnegative KSVD [3].",

author = "Robert Peharz and Michael Stark and Franz Pernkopf",

year = "2010",

month = nov,

day = "24",

doi = "10.1109/MLSP.2010.5589219",

language = "English",

isbn = "9781424478774",

pages = "83--88",

booktitle = "Proceedings of the 2010 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2010",

publisher = "Institute of Electrical and Electronics Engineers",

address = "United States",

note = "20th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2010, MLSP 2010 ; Conference date: 29-08-2010 Through 01-09-2010",

}

Peharz, R, Stark, M & Pernkopf, F 2010, Sparse nonnegative matrix factorization using ℓ⁰-constraints. in Proceedings of the 2010 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2010., 5589219, Institute of Electrical and Electronics Engineers, pp. 83-88, 20th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2010, Kittila, Finland, 29/08/10. https://doi.org/10.1109/MLSP.2010.5589219

Sparse nonnegative matrix factorization using ℓ⁰-constraints. / Peharz, Robert; Stark, Michael; Pernkopf, Franz.
Proceedings of the 2010 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2010. Institute of Electrical and Electronics Engineers, 2010. p. 83-88 5589219.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Sparse nonnegative matrix factorization using ℓ0-constraints

AU - Peharz, Robert

AU - Stark, Michael

AU - Pernkopf, Franz

N1 - Conference code: 20

PY - 2010/11/24

Y1 - 2010/11/24

N2 - Although nonnegative matrix factorization (NMF) favors a part-based and sparse representation of its input, there is no guarantee for this behavior. Several extensions to NMF have been proposed in order to introduce sparseness via the ℓ1-norm, while little work is done using the more natural sparseness measure, the ℓ0-pseudo-norm. In this work we propose two NMF algorithms with ℓ0-sparseness constraints on the bases and the coefficient matrices, respectively. We show that classic NMF [1] is a suited tool for ℓ0-sparse NMF algorithms, due to a property we call sparseness maintenance. We apply our algorithms to synthetic and real-world data and compare our results to sparse NMF [2] and nonnegative KSVD [3].

AB - Although nonnegative matrix factorization (NMF) favors a part-based and sparse representation of its input, there is no guarantee for this behavior. Several extensions to NMF have been proposed in order to introduce sparseness via the ℓ1-norm, while little work is done using the more natural sparseness measure, the ℓ0-pseudo-norm. In this work we propose two NMF algorithms with ℓ0-sparseness constraints on the bases and the coefficient matrices, respectively. We show that classic NMF [1] is a suited tool for ℓ0-sparse NMF algorithms, due to a property we call sparseness maintenance. We apply our algorithms to synthetic and real-world data and compare our results to sparse NMF [2] and nonnegative KSVD [3].

UR - http://www.scopus.com/inward/record.url?scp=78449280430&partnerID=8YFLogxK

U2 - 10.1109/MLSP.2010.5589219

DO - 10.1109/MLSP.2010.5589219

M3 - Conference contribution

AN - SCOPUS:78449280430

SN - 9781424478774

SP - 83

EP - 88

BT - Proceedings of the 2010 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2010

PB - Institute of Electrical and Electronics Engineers

T2 - 20th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2010

Y2 - 29 August 2010 through 1 September 2010

ER -

Sparse nonnegative matrix factorization using ℓ⁰-constraints

Abstract

Conference

Access to Document

Other files and links

Fingerprint

Cite this