Fast Parallel Randomized Algorithm for Nonnegative Matrix Factorization with KL Divergence for Large Sparse Datasets

Nonnegative Matrix Factorization (NMF) with Kullback-Leibler Divergence (NMF-KL) is one of the most significant NMF problems and equivalent to Probabilistic Latent Semantic Indexing (PLSI), which has been successfully applied in many applications. For sparse count data, a Poisson distribution and KL divergence provide sparse models and sparse representation, which describe the random variation better than a normal distribution and Frobenius norm. Specially, sparse models provide more concise understanding of the appearance of attributes over latent components, while sparse representation provides concise interpretability of the contribution of latent components over instances. However, minimizing NMF with KL divergence is much more difficult than minimizing NMF with Frobenius norm; and sparse models, sparse representation and fast algorithms for large sparse datasets are still challenges for NMF with KL divergence. In this paper, we propose a fast parallel randomized coordinate descent algorithm having fast convergence for large sparse datasets to archive sparse models and sparse representation. The proposed algorithm's experimental results overperform the current studies' ones in this problem

Toward a Robust Sparse Data Representation for Wireless Sensor Networks

Compressive sensing has been successfully used for optimized operations in wireless sensor networks. However, raw data collected by sensors may be neither originally sparse nor easily transformed into a sparse data representation. This paper addresses the problem of transforming source data collected by sensor nodes into a sparse representation with a few nonzero elements. Our contributions that address three major issues include: 1) an effective method that extracts population sparsity of the data, 2) a sparsity ratio guarantee scheme, and 3) a customized learning algorithm of the sparsifying dictionary. We introduce an unsupervised neural network to extract an intrinsic sparse coding of the data. The sparse codes are generated at the activation of the hidden layer using a sparsity nomination constraint and a shrinking mechanism. Our analysis using real data samples shows that the proposed method outperforms conventional sparsity-inducing methods.Comment: 8 page