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

TL;DR

This paper introduces a fast parallel randomized coordinate descent algorithm for Nonnegative Matrix Factorization with KL divergence, effectively handling large sparse datasets and improving convergence and performance over existing methods.

Contribution

The paper presents a novel fast parallel randomized algorithm for NMF-KL that achieves better convergence and scalability on large sparse datasets.

Findings

Outperforms existing methods in speed and accuracy

Achieves sparse models and representations efficiently

Effective for large-scale sparse data analysis

Abstract

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.