NMF, LNMF, and DNMF modeling of neural receptive fields involved in human facial expression perception

Recently, three learning algorithms, namely non-negative matrix factorization (NMF), local non-negative matrix factorization (LNMF), and discriminant non-negative matrix factorization (DNMF) have been proposed to produce sparse image representations. However, when their input is a database of human facial images, they decompose the images into sparse representations with quite different degree of sparseness. Within a continuum of sparseness ranging from holistic to local image representation, the first algorithm rather tends towards the first extreme, while the second algorithm produces a local representation. The third algorithm provides an image representation that is in between these two extremes. These algorithms decompose the facial images in the database into basis images and their corresponding coefficients. The basis images are learned by the algorithm when human face images are given as input. By analogy to neurophysiology, the basis images could be associated with the receptive fields of neuronal cells involved in encoding human faces. Taken from this point of view, the paper presents an analysis of these three representations in connection to the receptive field parameters such as spatial frequency, frequency orientation, position, length, width, aspect ratio, etc. By analyzing the tiling properties of these bases we can have an insight of how suitable these algorithms are to resemble biological visual perception systems.