Evaluation of Distance Measures For NMF-Based Face Image Applications

Non-negative matrix factorization (NMF) is an increasingly popular feature extraction method. Since it is designed to fit training samples using linear combination of non-negative basis vectors, it is particular suitable for image applications as it affords intuitive localized interpretations. However, in this space defined by the NMF basis images, there has not been any systematic research to identify suitable distance measure for NMF-based data classification. In this paper, the performance of 19 distance measures between feature vectors is evaluated based on the result of the NMF algorithm for face recognition, which include most of the standard distance measures used in face recognition, as well as two new non-negative vector similarity coefficient-based (NVSC) distances that we recommend for use in NMF-based pattern recognition. Recognition experiments are performed using the CMU AMP Face Expression database, CBCL2 database, MIT-CBCL database, YaleB database, and FERET database. We also compared the performance of NMF with Eigen-face method and showed that the NMF algorithm using the NVSC distance yielded the best recognition results.