A Projected Alternating Least square Approach for Computation of Nonnegative Matrix Factorization
Nonnegative matrix factorization (NMF) is a common method in data mining that have been used in different applications as a dimension reduction, classification or clustering method. Methods in alternating least square (ALS) approach usually used to solve this non-convex minimization problem. At eac...
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University of Tehran
2015-09-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
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| Online Access: | https://jsciences.ut.ac.ir/article_55315_2115c7b81a5e4728a3ff207a0a9574b6.pdf |
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| author | M. Rezghi M. Yousefi |
| author_facet | M. Rezghi M. Yousefi |
| author_sort | M. Rezghi |
| collection | DOAJ |
| description | Nonnegative matrix factorization (NMF) is a common method in data mining that have been used in different applications as a dimension reduction, classification or clustering method. Methods in alternating least square (ALS) approach usually used to solve this non-convex minimization problem. At each step of ALS algorithms two convex least square problems should be solved, which causes high computational cost. In this paper, based on the properties of norms and orthogonal transformations we propose a framework to project NMF’s convex sub-problems to smaller problems. This projection reduces the time of finding NMF factors. Also every method on ALS class can be used with our proposed framework. |
| format | Article |
| id | doaj-art-aadf2b6cc3ea4fbbbef1c12f3906d8a7 |
| institution | DOAJ |
| issn | 1016-1104 2345-6914 |
| language | English |
| publishDate | 2015-09-01 |
| publisher | University of Tehran |
| record_format | Article |
| series | Journal of Sciences, Islamic Republic of Iran |
| spelling | doaj-art-aadf2b6cc3ea4fbbbef1c12f3906d8a72025-08-20T03:13:36ZengUniversity of TehranJournal of Sciences, Islamic Republic of Iran1016-11042345-69142015-09-0126327327955315A Projected Alternating Least square Approach for Computation of Nonnegative Matrix FactorizationM. Rezghi0M. Yousefi1Department of Computer Science, Faculty of Sciences, Tarbiat Modares University, Tehran, Islamic Republic of IranDepartment of Applied Mathematics, Faculty of Sciences, Sahand University of Technology, Tabriz, Islamic Republic of IranNonnegative matrix factorization (NMF) is a common method in data mining that have been used in different applications as a dimension reduction, classification or clustering method. Methods in alternating least square (ALS) approach usually used to solve this non-convex minimization problem. At each step of ALS algorithms two convex least square problems should be solved, which causes high computational cost. In this paper, based on the properties of norms and orthogonal transformations we propose a framework to project NMF’s convex sub-problems to smaller problems. This projection reduces the time of finding NMF factors. Also every method on ALS class can be used with our proposed framework.https://jsciences.ut.ac.ir/article_55315_2115c7b81a5e4728a3ff207a0a9574b6.pdfnonnegative matrix factorizationalternating least squaresinitializationorthogonal transformation |
| spellingShingle | M. Rezghi M. Yousefi A Projected Alternating Least square Approach for Computation of Nonnegative Matrix Factorization Journal of Sciences, Islamic Republic of Iran nonnegative matrix factorization alternating least squares initialization orthogonal transformation |
| title | A Projected Alternating Least square Approach for Computation of Nonnegative Matrix Factorization |
| title_full | A Projected Alternating Least square Approach for Computation of Nonnegative Matrix Factorization |
| title_fullStr | A Projected Alternating Least square Approach for Computation of Nonnegative Matrix Factorization |
| title_full_unstemmed | A Projected Alternating Least square Approach for Computation of Nonnegative Matrix Factorization |
| title_short | A Projected Alternating Least square Approach for Computation of Nonnegative Matrix Factorization |
| title_sort | projected alternating least square approach for computation of nonnegative matrix factorization |
| topic | nonnegative matrix factorization alternating least squares initialization orthogonal transformation |
| url | https://jsciences.ut.ac.ir/article_55315_2115c7b81a5e4728a3ff207a0a9574b6.pdf |
| work_keys_str_mv | AT mrezghi aprojectedalternatingleastsquareapproachforcomputationofnonnegativematrixfactorization AT myousefi aprojectedalternatingleastsquareapproachforcomputationofnonnegativematrixfactorization AT mrezghi projectedalternatingleastsquareapproachforcomputationofnonnegativematrixfactorization AT myousefi projectedalternatingleastsquareapproachforcomputationofnonnegativematrixfactorization |