Generalized Low-Rank Approximations
We study the frequent problem of approximating a target matrix with a matrix of lower rank. We provide a simple and efficient (EM) algorithm for solving {\\em weighted} low rank approximation problems, which, unlike simple matrix factorization problems, do not admit a closed form solution in general...
| Main Authors: | , |
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| Language: | en_US |
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2004
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| Online Access: | http://hdl.handle.net/1721.1/6708 |
| _version_ | 1826213217926381568 |
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| author | Srebro, Nathan Jaakkola, Tommi |
| author_facet | Srebro, Nathan Jaakkola, Tommi |
| author_sort | Srebro, Nathan |
| collection | MIT |
| description | We study the frequent problem of approximating a target matrix with a matrix of lower rank. We provide a simple and efficient (EM) algorithm for solving {\\em weighted} low rank approximation problems, which, unlike simple matrix factorization problems, do not admit a closed form solution in general. We analyze, in addition, the nature of locally optimal solutions that arise in this context, demonstrate the utility of accommodating the weights in reconstructing the underlying low rank representation, and extend the formulation to non-Gaussian noise models such as classification (collaborative filtering). |
| first_indexed | 2024-09-23T15:45:20Z |
| id | mit-1721.1/6708 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:45:20Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | mit-1721.1/67082019-04-12T08:31:52Z Generalized Low-Rank Approximations Srebro, Nathan Jaakkola, Tommi AI svd pca We study the frequent problem of approximating a target matrix with a matrix of lower rank. We provide a simple and efficient (EM) algorithm for solving {\\em weighted} low rank approximation problems, which, unlike simple matrix factorization problems, do not admit a closed form solution in general. We analyze, in addition, the nature of locally optimal solutions that arise in this context, demonstrate the utility of accommodating the weights in reconstructing the underlying low rank representation, and extend the formulation to non-Gaussian noise models such as classification (collaborative filtering). 2004-10-08T20:38:40Z 2004-10-08T20:38:40Z 2003-01-15 AIM-2003-001 http://hdl.handle.net/1721.1/6708 en_US AIM-2003-001 10 p. 2061103 bytes 911431 bytes application/postscript application/pdf application/postscript application/pdf |
| spellingShingle | AI svd pca Srebro, Nathan Jaakkola, Tommi Generalized Low-Rank Approximations |
| title | Generalized Low-Rank Approximations |
| title_full | Generalized Low-Rank Approximations |
| title_fullStr | Generalized Low-Rank Approximations |
| title_full_unstemmed | Generalized Low-Rank Approximations |
| title_short | Generalized Low-Rank Approximations |
| title_sort | generalized low rank approximations |
| topic | AI svd pca |
| url | http://hdl.handle.net/1721.1/6708 |
| work_keys_str_mv | AT srebronathan generalizedlowrankapproximations AT jaakkolatommi generalizedlowrankapproximations |