Computational decomposition of molecular signatures based on blind source separation of non-negative dependent sources with NMF

As a common feature in microarray profiling, gene expression profiles represent a composite of more than one distinct sources, which can severely decrease the sensitivity and specificity for the measurement of molecular signatures associated with different disease processes. Independent component analysis (ICA) is a widely applicable approach in blind source separation (BSS) but with limitations that the sources are independent, while a more common situation, which still happens in microarray profiles, is BSS where sources are not statistically independent. A novel idea of BSS is presented: it is a matrix factorization problem without enforcement of statistical characteristics on sources, while blind independent source separation is in fact matrix factorization, to factorize the observation matrix into a mixing matrix and a source matrix where the sources are independent. Since non-negative sources are meaningful in many applications including microarray profiling, we presented that blind non-negative source separation is essentially a matrix factorization, to factorize the observation matrix into a non-negative mixing matrix and a non-negative source matrix where the sources may be dependent. Non-negative matrix factorization (NMF) technique is applied to this non-negative source separation and is proven by a large number of computer simulations and by partial volume correction (PVC) experiments for real microarray data that it is effective when the sources are dependent with each other and/or are Gaussian distributed.