Low-rank approximations allow for compact representations of data with reduced storage and runtime requirements and reduced redundancy and noise. The Non-negative Matrix Factorization (NMF) is a special low-rank approximation which allows for additive parts-based, interpretable representation of the data. Various properties of NMF are similar to Swarm Intelligence (SI) methods: indeed, most NMF objective functions and most SI fitness functions are non-convex, discontinuous, and may possess many local minima. This chapter summarizes our efforts on improving convergence, approximation quality, and classification accuracy of NMF using five different meta-heuristics based on SI and evolutionary computation. We present (i) new initialization strategies for NMF, and (ii) an iterative update strategy for NMF. The applicability of our approach is illustrated on data sets coming from the areas of spam filtering and email classification. Experimental results show that both optimization strategies are able to improve NMF in terms of faster convergence, lower approximation error, and/or better classification accuracy.

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