New iterative approach (ISNCA) for constrained matrix factorization methods

Gene regulation networks are complex, often involve thousands of genes, regulators and the connections between them. To understand the complex interactions between these genes and regulators with time, large empirical data is used the so called time-series gene expression data. Many statistical tools are used to analyze this data but they often impose restrictions that reduce the size of the network and make the solution less feasible from a biological perspective. We developed the iterative subnetwork component analysis (ISNCA), a method that decomposes the empirical data of two or more overlapping subnetworks with joint components at one iteration, and updates the solution at the next iteration by subtracting the contribution of each of the subnetworks. This predict - update method managed to relax the restrictions and solve larger networks. We generalized the method in this paper to include both regulators and genes in the joint partition, and demonstrated its accuracy using a synthetic network with a known matrix decomposition. We also applied the ISNCA on large biological data taken from mice cells and obtained larger and more accurate solutions than achieved by previous methods.