Fast Parallel Randomized Algorithm for Nonnegative Matrix Factorization with KL Divergence for Large Sparse Datasets
This work addresses the need for scalable and interpretable factorization techniques in applications like text analysis, though it appears incremental as it builds on prior NMF-KL methods.
The authors tackled the challenge of efficiently solving Nonnegative Matrix Factorization with Kullback-Leibler Divergence for large sparse datasets, proposing a fast parallel randomized coordinate descent algorithm that outperforms existing methods in experimental results.
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.