Recently we have learned about a variety of matrix factoring techniques (LU, SVD, etc). One particular form, Non-negative matrix factorization, has found an application in cancer research. Multiple myeloma is a cancer that affects the bone marrow, and particularly plasma cells. Plasma cells produce a large amount of the antibodies which the body uses to fight infection. The cells proliferate and cause further genetic abnormalities throughout the body.

Fortunately, research is leading to improved treatments. Scientists at the Dana-Farber institute have investigated the genome of myeloma cells, looking for specific genetic subtypes to target with treatments. Researchers used a technique called comparative genomic hybridization to compare healthy blood cells with myeloma cells. After altered genetic types were singled out, researches needed to group these results based on similarity, so as to classify the different markers. To do so, researches used an algorithm based on facial mapping algorithms, using non-negative matrix factorization (NMF).

NMF differs in other factorization techniques we have learned in that it satisfies the constraint that the factorization matrices of a given matrix consist of non-negative entries. NMF was originally proposed to assist in the decomposition of images, and has also found application in text mining and spectral data analysis (e.g. identifying space debris). In the Dana-Farber research, NMF was used to identify the particulars of myeloma cells, similar to identifying distinct facial features in people. NMF analysis led to the identification of four genetic subtypes of myeloma which could be specifically targeted by treatments.

Check out the original article to read further about the research and the treatments it makes possible.

Resources
http://www.sciencedaily.com/releases/2006/04/060410162109.htm
http://en.wikipedia.org/wiki/Multiple_myeloma
http://en.wikipedia.org/wiki/NMF