Evaluation of distance measures for NMF-based face recognition

Non-negative matrix factorization (NMF) is an unsupervised learning algorithm that can extract parts from visual data. The goal of this technique is to find intuitive basis such that training examples can be faithfully reconstructed using linear combination of basis images which are restricted to non-negative values. Thus NMF basis images can be understood as localized features that correspond better with intuitive notions of parts of images. However, there has not been any systematic study to identify suitable distance measure for data classification in this space defined by the NMF basis images. In this article we evaluate the performance of 17 distance measures (which include most of the standard distance measures used in face recognition, as well as a new non-negative vector similarity coefficient-based (NVSC) distance that we advocate for use in NMF-based pattern recognition) between feature vectors based on the result of the non-negative matrix factorization (NMF) algorithm for face recognition. Recognition experiments are performed using the MIT-CBCL database, CMU AMP Face Expression database and YaleB database. The experiments show, that our NVSC distance is consistently among the best measures with respect to different databases. Moreover, using this new distance, we almost always achieve better result than the L1, L2 and Mahalanobis distance which are often used in pattern recognition.