Integrative Analysis of Many Weighted Co-Expression Networks Using Tensor Computation

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

A primer on correlation-based dimension reduction methods for multi-omics analysis

The continuing advances of omic technologies mean that it is now more tangible to measure the numerous features collectively reflecting the molecular properties of a sample. When multiple omic methods are used, statistical and computational approaches can exploit these large, connected profiles. Multi-omics is the integration of different omic data sources from the same biological sample. In this review, we focus on correlation-based dimension reduction approaches for single omic datasets, followed by methods for pairs of omics datasets, before detailing further techniques for three or more omic datasets. We also briefly detail network methods when three or more omic datasets are available and which complement correlation-oriented tools. To aid readers new to this area, these are all linked to relevant R packages that can implement these procedures. Finally, we discuss scenarios of experimental design and present road maps that simplify the selection of appropriate analysis methods. This review will guide researchers navigate the emerging methods for multi-omics and help them integrate diverse omic datasets appropriately and embrace the opportunity of population multi-omics.Comment: 30 pages, 2 figures, 6 table

Altered Topological Structure of the Brain White Matter in Maltreated Children through Topological Data Analysis

Childhood maltreatment may adversely affect brain development and consequently influence behavioral, emotional, and psychological patterns during adulthood. In this study, we propose an analytical pipeline for modeling the altered topological structure of brain white matter in maltreated and typically developing children. We perform topological data analysis (TDA) to assess the alteration in the global topology of the brain white-matter structural covariance network among children. We use persistent homology, an algebraic technique in TDA, to analyze topological features in the brain covariance networks constructed from structural magnetic resonance imaging (MRI) and diffusion tensor imaging (DTI). We develop a novel framework for statistical inference based on the Wasserstein distance to assess the significance of the observed topological differences. Using these methods in comparing maltreated children to a typically developing control group, we find that maltreatment may increase homogeneity in white matter structures and thus induce higher correlations in the structural covariance; this is reflected in the topological profile. Our findings strongly suggest that TDA can be a valuable framework to model altered topological structures of the brain. The MATLAB codes and processed data used in this study can be found at https://github.com/laplcebeltrami/maltreated

Matrix and Tensor Factorization Methods for Toxicogenomic Modeling and Prediction

Peer reviewe