A somewhat dated, but still relevant article published in Nature magazine describes how non-negative matrix factorization (NMF) can be used in object, and specifically, facial recognition.  While many other methods of facial recognition perform comparison analysis on the face as a whole (using, say, the eigenfaces talked about in a previous blog entry), the non-negative property of NMF allows a system to deal with only specific parts of a face.  Essentially, the technique presented learns its basis by examining parts of a face and since the matrix representing faces contains only positive values, a face becomes the sum of these parts.  In processing the known images, database of known face images is represented in a matrix, V; the basis images in another matrix, W, and a third matrix, H, with unary columns represents a one-to-one mapping of faces to a corresponding face in V.  The factorization is thus V=WH, where the matrices W and H compress the data found in V.  This compression allows for faster interpretation relative to V of whether or not a given image is similar to those present in V.  While NMF speeds up these recognition techniques by providing faster comparisons with a known database, the authors also present other uses of NMF.  These include semantic analysis of text (described in another blog entry), and other databases where the core data isn’t widely varied. 

Source: http://www.nature.com/nature/journal/v401/n6755/full/401788a0.html