title: Integrative analysis of many weighted co-expression networks using tensor computation.
abstract: The rapid accumulation of biological networks poses new challenges and calls for powerful integrative analysis tools. Most existing methods capable of simultaneously analyzing a large number of networks were primarily designed for unweighted networks, and cannot easily be extended to weighted networks. However, it is known that transforming weighted into unweighted networks by dichotomizing the edges of weighted networks with a threshold generally leads to information loss. We have developed a novel, tensor-based computational framework for mining recurrent heavy subgraphs in a large set of massive weighted networks. Specifically, we formulate the recurrent heavy subgraph identification problem as a heavy 3D subtensor discovery problem with sparse constraints. We describe an effective approach to solving this problem by designing a multi-stage, convex relaxation protocol, and a non-uniform edge sampling technique. We applied our method to 130 co-expression networks, and identified 11,394 recurrent heavy subgraphs, grouped into 2,810 families. We demonstrated that the identified subgraphs represent meaningful biological modules by validating against a large set of compiled biological knowledge bases. We also showed that the likelihood for a heavy subgraph to be meaningful increases significantly with its recurrence in multiple networks, highlighting the importance of the integrative approach to biological network analysis. Moreover, our approach based on weighted graphs detects many patterns that would be overlooked using unweighted graphs. In addition, we identified a large number of modules that occur predominately under specific phenotypes. This analysis resulted in a genome-wide mapping of gene network modules onto the phenome. Finally, by comparing module activities across many datasets, we discovered high-order dynamic cooperativeness in protein complex networks and transcriptional regulatory networks.
authors.affiliation: Molecular and Computational Biology, Department of Biological Sciences, University of Southern California, Los Angeles, California, USA.
authors.forename: Wenyuan
authors.initials: W
authors.lastname: Li
authors.forename: Chun-Chi
authors.initials: CC
authors.lastname: Liu
authors.forename: Tong
authors.initials: T
authors.lastname: Zhang
authors.forename: Haifeng
authors.initials: H
authors.lastname: Li
authors.forename: Michael S
authors.initials: MS
authors.lastname: Waterman
authors.forename: Xianghong Jasmine
authors.initials: XJ
authors.lastname: Zhou
mesh_terms: D000465:Algorithms; D019295:Computational Biology / Q000379:methods*; D030541:Databases, Genetic; D030562:Databases, Protein; D015870:Gene Expression; D005786:Gene Expression Regulation; D053263:Gene Regulatory Networks; D006801:Humans; D008957:Models, Genetic; D020411:Oligonucleotide Array Sequence Analysis; D010641:Phenotype; D011506:Proteins; D012815:Signal Processing, Computer-Assisted
chemical_list: D011506:Proteins