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Non-Negative Matrix Factorization via Low-Rank Stochastic Manifold Optimization

Douik, Ahmed and Hassibi, Babak (2019) Non-Negative Matrix Factorization via Low-Rank Stochastic Manifold Optimization. In: 2019 IEEE International Symposium on Information Theory (ISIT). IEEE , Piscataway, NJ, pp. 497-501. ISBN 9781538692912. https://resolver.caltech.edu/CaltechAUTHORS:20191004-100332012

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Abstract

Several real-world applications, notably in non-negative matrix factorization, graph-based clustering, and machine learning, require solving a convex optimization problem over the set of stochastic and doubly stochastic matrices. A common feature of these problems is that the optimal solution is generally a low-rank matrix. This paper suggests reformulating the problem by taking advantage of the low-rank factorization X = UV^T and develops a Riemannian optimization framework for solving optimization problems on the set of low-rank stochastic and doubly stochastic matrices. In particular, this paper introduces and studies the geometry of the low-rank stochastic multinomial and the doubly stochastic manifold in order to derive first-order optimization algorithms. Being carefully designed and of lower dimension than the original problem, the proposed Riemannian optimization framework presents a clear complexity advantage. The claim is attested through numerical experiments on real-world and synthetic data for Non-negative Matrix Factorization (NFM) applications. The proposed algorithm is shown to outperform, in terms of running time, state-of-the-art methods for NFM.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/isit.2019.8849441DOIArticle
ORCID:
AuthorORCID
Douik, Ahmed0000-0001-7791-9443
Additional Information:© 2019 IEEE.
Record Number:CaltechAUTHORS:20191004-100332012
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20191004-100332012
Official Citation:A. Douik and B. Hassibi, "Non-Negative Matrix Factorization via Low-Rank Stochastic Manifold Optimization," 2019 IEEE International Symposium on Information Theory (ISIT), Paris, France, 2019, pp. 497-501. doi: 10.1109/ISIT.2019.8849441
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99072
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:04 Oct 2019 17:43
Last Modified:04 Oct 2019 17:43

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