Determining a suitable metric when using non-negative matrix factorization

The Non-negative Matrix Factorization technique (NMF) has been recently proposed for dimensionality reduction. NMF is able to produce a region- or part-based representation of objects and images. The positive space defined with NMF lacks a suitable metric and this paper experimentally compares NMF to Principal Component Analysis (PCA) in the context of classification, trying to determine the best distance metric for NMF. This paper introduces the use of the Earth Mover´s Distance (EMD) as a relevant metric that takes into account the positive definition of the NMF bases, leading to better recognition results when the dimensionality of the problem is correctly chosen. PCA and NMF have also been tested under the presence of occlusions and, due to its part-based representation, NMF is able to improve on the PCA results.