Non-matrix factorization has many applications. One of them aforementioned is in facial recognition. There are several applications in medicine. One technique called CGH or comparative genomic hybridization has been used to analyze samples from patients with myeloma and has aided in the identifications of four genetic subtype. This was done using a algorithm using non-negative matrix factorization. This narrowing of genes is an advance that will aid in design of therapeutics and so forth.
Non-matrix factorizatin is also being used in algorithms such as expression programs where biological pathways can be determined. This allows for organizing and designing experiments of biological importance. There have been gene expression programs determining important pathways already. In some areas, genes for diseases have been identified as aforementioned. This will as mentioned allow for design of clinical and biological experiments.
An interesting algorithm involves studying cell lines by reducing genes to a handful of metagenes. Reducing the thousands of genes to a small number of metagenes allows for studying the various clusters of genes. A data set usually consists of N genes in M samples. The expression matrix A is of dimensions N x M. This matrix in this algorithm is factored to a A ~ WH. W is of dimensions N x k with k being a metagene entry and H is k x M representing the metagene expression. This studies different clusters. However there are still issues of this to be dealt with due to its complexity. A graphic below shows the clustering of genes into 2 clusters. 
Several other uses exist which can help elucidate mechanisms and so forth and reduce costs of experiments and testing as well as the time it takes to develop certain drugs.
References
http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030148
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