Robust Large Scale Non-negative Matrix Factorization using Proximal Point Algorithm
This work addresses scalability and robustness issues in NMF for applications like data analysis, but it appears incremental as it builds on prior LP methods with specific modifications.
The paper tackles the problem of robust large-scale non-negative matrix factorization (NMF) under separability assumptions, presenting an algorithm that modifies a Linear Programming approach by reducing constraints and eliminating the need to know the factorization rank, with performance evaluated on synthetic datasets.
A robust algorithm for non-negative matrix factorization (NMF) is presented in this paper with the purpose of dealing with large-scale data, where the separability assumption is satisfied. In particular, we modify the Linear Programming (LP) algorithm of [9] by introducing a reduced set of constraints for exact NMF. In contrast to the previous approaches, the proposed algorithm does not require the knowledge of factorization rank (extreme rays [3] or topics [7]). Furthermore, motivated by a similar problem arising in the context of metabolic network analysis [13], we consider an entirely different regime where the number of extreme rays or topics can be much larger than the dimension of the data vectors. The performance of the algorithm for different synthetic data sets are provided.