Affiliation:
1. Clemson University, Clemson, SC
2. Colorado School of Mines, Golden, CO
3. University of Denver, Denver, CO
Abstract
Nonnegative Matrix Factorization (NMF) is broadly used to determine class membership in a variety of clustering applications. From movie recommendations and image clustering to visual feature extractions, NMF has applications to solve a large number of knowledge discovery and data mining problems. Traditional optimization methods, such as the Multiplicative Updating Algorithm (MUA), solves the NMF problem by utilizing an auxiliary function to ensure that the objective monotonically decreases. Although the objective in MUA converges, there exists no proof to show that the learned matrix factors converge as well. Without this rigorous analysis, the clustering performance and stability of the NMF algorithms cannot be guaranteed. To address this knowledge gap, in this article, we study the factor-bounded NMF problem and provide a solution algorithm with proven convergence by rigorous mathematical analysis, which ensures that both the objective and matrix factors converge. In addition, we show the relationship between MUA and our solution followed by an analysis of the convergence of MUA. Experiments on both toy data and real-world datasets validate the correctness of our proposed method and its utility as an effective clustering algorithm.
Funder
National Science Foundation
Publisher
Association for Computing Machinery (ACM)
Reference41 articles.
1. On the convergence of the proximal algorithm for nonsmooth functions involving analytic features;Attouch Hedy;Mathematical Programming,2009
2. Convergence of descent methods for semi-algebraic and tame problems: Proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods;Attouch Hedy;Mathematical Programming,2013
3. The Łojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems;Bolte Jérôme;SIAM Journal on Optimization,2007
4. Graph regularized nonnegative matrix factorization for data representation;Cai Deng;IEEE Transactions on Pattern Analysis and Machine Intelligence,2011
5. Projected gradient methods for linearly constrained problems;Calamai Paul H.;Mathematical Programming,1987
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