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A Fast Non-Smooth Nonnegative Matrix Factorization for Learning Sparse Representation
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DOI：10.1109/ACCESS.2016.2605704.png)
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摘要
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Nonnegative matrix factorization (NMF) is a hot topic in machine learning and data processing. Recently, a constrained version, non-smooth NMF (NsNMF), shows a great potential in learning meaningful sparse representation of the observed data. However, it suffers from a slow linear convergence rate, discouraging its applications to large-scale data representation. In this paper, a fast NsNMF (FNsNMF) algorithm is proposed to speed up NsNMF. In the proposed method, it first shows that the cost function of the derived sub-problem is convex and the corresponding gradient is Lipschitz continuous. Then, the optimization to this function is replaced by solving a proximal function, which is designed based on the Lipschitz constant and can be solved through utilizing a constructed fast convergent sequence. Due to the usage of the proximal function and its efficient optimization, our method can achieve a nonlinear convergence rate, much faster than NsNMF. Simulations in both computer generated data and the real-world data show the advantages of our algorithm over the compared methods.
Keyword:
Nonnegative matrix factorization
sparse representation
nonlinear convergence rate
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3.6
论文数:
9.8W
被引数:
29.4W
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