A comparative study of NMF, DNMF, and LNMF algorithms applied for face recognition

Three techniques called non-negative matrix factorization (NMF), local non-negative matrix factorization (LNMF), and discriminant non-negative matrix factorization (DNMF), have been recently developed for decomposing a data matrix into non-negative factors named basis images and decomposition coefficients. Although these techniques are closely related to each other since they impose certain common non-negative constraints, the decomposition process of each algorithm involves a different objective function. While NMF approximates in the best possible way the data matrix by the product of its decomposition factors imposing only nonnegative constraints, LNMF adds more constraints on the basis images to reduce the redundant information between them and to enlarge their sparseness degree. DNMF imposes more constraints on the coefficients in order to take into account class information. In this paper these methods are used in the context of face recognition to extract features from two image databases (YALE and ORL). Extracted features are further classified by two metric-based classifiers, namely Maximum Correlation Classifier (MCC) and Cosine Similarity Measure (CSM). Besides, Support Vector Machines (SVMs) are also used for classification. Experiments show that when these algorithms are applied along with the aforementioned classifiers, to face recognition task they lead to quite different results, their performance being data dependent.