We describe the use of the matrix eigenvalue decomposition (EVD) and pseudoinverse projection and a tensor higher-order EVD (HOEVD) in reconstructing the pathways that compose a cellular system from genome-scale nondirectional networks of correlations among the genes of the system. The EVD formulates a genes x genes network as a linear superposition of genes x genes decorrelated and decoupled rank-1 subnetworks, which can be associated with functionally independent pathways. The integrative pseudoinverse projection of a network computed from a "data" signal onto a designated "basis" signal approximates the network as a linear superposition of only the subnetworks that are common to both signals and simulates observation of only the pathways that are manifest in both experiments. We define a comparative HOEVD that formulates a series of networks as linear superpositions of decorrelated rank-1 subnetworks and the rank-2 couplings among these subnetworks, which can be associated with independent pathways and the transitions among them common to all networks in the series or exclusive to a subset of the networks. Boolean functions of the discretized subnetworks and couplings highlight differential, i.e., pathway-dependent, relations among genes. We illustrate the EVD, pseudoinverse projection, and HOEVD of genome-scale networks with analyses of yeast DNA microarray data.
|Evidence ID||Analyze ID||Interactor||Interactor Systematic Name||Interactor||Interactor Systematic Name||Type||Assay||Annotation||Action||Modification||Phenotype||Source||Reference||Note|
|Evidence ID||Analyze ID||Gene||Gene Systematic Name||Gene Ontology Term||Gene Ontology Term ID||Qualifier||Aspect||Method||Evidence||Source||Assigned On||Reference||Annotation Extension|
|Evidence ID||Analyze ID||Gene||Gene Systematic Name||Phenotype||Experiment Type||Experiment Type Category||Mutant Information||Strain Background||Chemical||Details||Reference|
|Evidence ID||Analyze ID||Regulator||Regulator Systematic Name||Target||Target Systematic Name||Experiment||Conditions||Strain||Source||Reference|