Fig. 3

Model-based integration of whole-genomic profiles and a molecular network. a The patient genomic profiles X along with the clinical information: the survival time, two patient subgroups for classification and treatment response of each individual patient are shown. The network S is typically integrated into the genomic profile analysis with a graph Laplacian regularization. The formulas of the graph Laplacian and its regularization are shown below. The graph Laplacian regularization can be rewritten as summation of pairwise smoothness terms that promote smoothness among the connected genomic features in the network. b The network-based linear regression and Cox regression models are illustrated in the figure with the graph Laplacian regularization term added to the original cost functions. c Network-based classification is illustrated by a network-based SVM to classify the samples. d Network-based semi-supervised learning models classify samples and detect disease markers on a bipartite graph. The edges between samples and genomic features are weighted by the genomic profiles, and semi-supervised learning is based on the bipartite graph Laplacian. e Network-based factorization models factorize the genomic profile X into the product of two matrices, U and H, which cluster patient samples and learn the latent features in the genomic profiles