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• W3003759898 abstract "In this paper we propose a quasi-Newton algorithm for the celebrated nonnegative matrix factorization (NMF) problem. The proposed algorithm falls into the general framework of Gauss-Newton and Levenberg-Marquardt methods. However, these methods were not able to handle constraints, which is present in NMF. One of the key contributions in this paper is to apply alternating direction method of multipliers (ADMM) to obtain the iterative update from this GaussNewton-like algorithm. Furthermore, we carefully study the structure of the Jacobian Gramian matrix given by the Gauss-Newton updates, and designed a way of exactly inverting the matrix with complexity O(mnk), which is a significant reduction compared to the naive implementation of complexity O((m + n) <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>3</sup> k <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>3</sup> ). The resulting algorithm, which we call NLS-ADMM, enjoys fast convergence rate brought by the quasi-Newton algorithmic framework, while maintaining low per-iteration complexity similar to that of alternating algorithms. Numerical experiments on synthetic data confirms the efficiency of our proposed algorithm." @default.
• W3003759898 created "2020-02-07" @default.
• W3003759898 creator A5002695199 @default.
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• W3003759898 date "2019-11-01" @default.
• W3003759898 modified "2023-10-16" @default.
• W3003759898 title "Low-complexity Proximal Gauss-Newton Algorithm for Nonnegative Matrix Factorization" @default.
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• W3003759898 doi "https://doi.org/10.1109/globalsip45357.2019.8969492" @default.
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