Evolutionary Nonnegative Matrix Factorization for Data Compression

Abstract. This paper aims at improving non-negative matrix factorization (NMF) to facilitate data compression. An evolutionary updating strategy is proposed to solve the NMF problem iteratively based on three sets of updating rules including multiplicative, firefly and survival of the fittest rules. For data compression application, the quality of the factorized matrices can be evaluated by measurements such as sparsity, orthogonality and factorization error to assess compression quality in terms of storage space consumption, redundancy in data matrix and data approximation accuracy. Thus, the fitness score function that drives the evolving procedure is designed as a composite score that takes into account all these measurements. A hybrid initialization scheme is performed to improve the rate of convergence, allowing multiple initial candidates generated by different types of NMF initialization approaches. Effectiveness of the proposed method is demonstrated using Yale and ORL image datasets.