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Conference Paper: Provable alternating gradient descent for non-negative matrix factorization with strong correlations
Title | Provable alternating gradient descent for non-negative matrix factorization with strong correlations |
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Authors | |
Issue Date | 2017 |
Citation | 34th International Conference on Machine Learning, ICML 2017, 2017, v. 5, p. 3233-3265 How to Cite? |
Abstract | Non-negative matrix factorization is a basic tool for decomposing data into the feature and weight matrices under non-negativity constraints, and in practice is often solved in the alternating minimization framework. However, it is unclear whether such algorithms can recover the ground-truth feature matrix when the weights for different features are highly correlated, which is common in applications. This paper proposes a simple and natural alternating gradient descent based algorithm, and shows that with a mild initialization it provably recovers the ground-truth in the presence of strong correlations. In most interesting cases, the correlation can be in the same order as the highest possible. Our analysis also reveals its several favorable features including robustness to noise. We complement our theoretical results with empirical studies on semi-synthetic datasets, demonstrating its advantage over several popular methods in recovering the ground-truth. |
Persistent Identifier | http://hdl.handle.net/10722/341224 |
DC Field | Value | Language |
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dc.contributor.author | Li, Yuanzhi | - |
dc.contributor.author | Liang, Yingyu | - |
dc.date.accessioned | 2024-03-13T08:41:08Z | - |
dc.date.available | 2024-03-13T08:41:08Z | - |
dc.date.issued | 2017 | - |
dc.identifier.citation | 34th International Conference on Machine Learning, ICML 2017, 2017, v. 5, p. 3233-3265 | - |
dc.identifier.uri | http://hdl.handle.net/10722/341224 | - |
dc.description.abstract | Non-negative matrix factorization is a basic tool for decomposing data into the feature and weight matrices under non-negativity constraints, and in practice is often solved in the alternating minimization framework. However, it is unclear whether such algorithms can recover the ground-truth feature matrix when the weights for different features are highly correlated, which is common in applications. This paper proposes a simple and natural alternating gradient descent based algorithm, and shows that with a mild initialization it provably recovers the ground-truth in the presence of strong correlations. In most interesting cases, the correlation can be in the same order as the highest possible. Our analysis also reveals its several favorable features including robustness to noise. We complement our theoretical results with empirical studies on semi-synthetic datasets, demonstrating its advantage over several popular methods in recovering the ground-truth. | - |
dc.language | eng | - |
dc.relation.ispartof | 34th International Conference on Machine Learning, ICML 2017 | - |
dc.title | Provable alternating gradient descent for non-negative matrix factorization with strong correlations | - |
dc.type | Conference_Paper | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.scopus | eid_2-s2.0-85048460183 | - |
dc.identifier.volume | 5 | - |
dc.identifier.spage | 3233 | - |
dc.identifier.epage | 3265 | - |