Evaluation of distance metrics for recognition based on non-negative matrix factorization

Non-negative matrix factorization (NMF) is an unsupervised algorithm that presents the ability of learning parts from visual data. The goal of this technique is to find basis functions such that training examples can be faithfully reconstructed using appropriate combinations of the discovered basis functions. Bases are restricted to non-negative values, and original data is represented by additive combinations of the basis vectors. The space defined by NMF basis lacks of a suitable metric. The aim of this paper is to explore different distance metrics for NMF in the context of statistical classification of objects, and to compare these results to those obtained with a related algorithm: principal component analysis (PCA). We evaluate Earth mover's distance as a relevant metric that takes into account the positive definition of the NMF bases, and it presents the best recognition rates when the dimensionality of data is correctly estimated. We also show that NMF outperforms PCA-based representation when visual data can be partially occluded. (C) 2002 Elsevier Science B.V. All rights reserved.