An optimal pairwise merge algorithm improves the quality and consistency of nonnegative matrix factorization
This addresses the issue of solution quality and consistency in NMF for researchers and practitioners in fields like source separation and feature extraction, though it appears incremental as an enhancement to existing algorithms.
The paper tackles the problem of non-negative matrix factorization (NMF) algorithms converging to poor local minima or inconsistent solutions by introducing a pairwise merge strategy in a higher-dimensional feature space. The method helps solutions escape to better local optima with greater consistency while maintaining similar computational performance to established methods.
Non-negative matrix factorization (NMF) is a key technique for feature extraction and widely used in source separation. However, existing algorithms may converge to poor local minima, or to one of several minima with similar objective value but differing feature parametrizations. Here we show that some of these weaknesses may be mitigated by performing NMF in a higher-dimensional feature space and then iteratively combining components with an analytically-solvable pairwise merge strategy. Experimental results demonstrate our method helps non-ideal NMF solutions escape to better local optima and achieve greater consistency of the solutions. Despite these extra steps, our approach exhibits similar computational performance to established methods by reducing the occurrence of "plateau phenomenon" near saddle points. Moreover, the results also illustrate that our method is compatible with different NMF algorithms. Thus, this can be recommended as a preferred approach for most applications of NMF.