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A unified framework for sparse non-negative least squares using multiplicative updates and the non-negative matrix factorization problem

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标题: A unified framework for sparse non-negative least squares using multiplicative updates and the non-negative matrix factorization problem
资源摘要: Publication date: May 2018
Source:Signal Processing, Volume 146

Author(s): Igor Fedorov, Alican Nalci, Ritwik Giri, Bhaskar D. Rao, Truong Q. Nguyen, Harinath Garudadri

We study the sparse non-negative least squares (S-NNLS) problem. S-NNLS occurs naturally in a wide variety of applications where an unknown, non-negative quantity must be recovered from linear measurements. We present a unified framework for S-NNLS based on a rectified power exponential scale mixture prior on the sparse codes. We show that the proposed framework encompasses a large class of S-NNLS algorithms and provide a computationally efficient inference procedure based on multiplicative update rules. Such update rules are convenient for solving large sets of S-NNLS problems simultaneously, which is required in contexts like sparse non-negative matrix factorization (S-NMF). We provide theoretical justification for the proposed approach by showing that the local minima of the objective function being optimized are sparse and the S-NNLS algorithms presented are guaranteed to converge to a set of stationary points of the objective function. We then extend our framework to S-NMF, showing that our framework leads to many well known S-NMF algorithms under specific choices of prior and providing a guarantee that a popular subclass of the proposed algorithms converges to a set of stationary points of the objective function. Finally, we study the performance of the proposed approaches on synthetic and real-world data.





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资源来源机构: Elsevier
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