NetSHy: network summarization via a hybrid approach leveraging topological properties

Abstract

Motivation Biological networks can provide a system level understanding of underlying processes. In many contexts, networks have a high degree of modularity, i.e., they consist of subsets of nodes, often known as subnetworks or modules, which are highly interconnected and may perform separate functions. In order to perform subsequent analyses to investigate the association between the identified module and a variable of interest, a module summarization, that best explains the module’s information and reduces dimensionality is often needed. Conventional approaches for obtaining network representation typically rely only on the profiles of the nodes within the network while disregarding the inherent network topological information. Results In this article, we propose NetSHy, a hybrid approach which is capable of reducing the dimension of a network while incorporating topological properties to aid the interpretation of the downstream analyses. In particular, NetSHy applies principal component analysis (PCA) on a combination of the node profiles and the well-known Laplacian matrix derived directly from the network similarity matrix to extract a summarization at a subject level. Simulation scenarios based on random and empirical networks at varying network sizes and sparsity levels show that NetSHy outperforms the conventional PCA approach applied directly on node profiles, in terms of recovering the true correlation with a phenotype of interest and maintaining a higher amount of explained variation in the data when networks are relatively sparse. The robustness of NetSHy is also demonstrated by more consistent correlation with the observed phenotype as the sample size decreases. Lastly, a genome wide association study (GWAS) is performed as an application of a downstream analysis, where NetSHy summarization scores on the biological networks identify more significant single nucleotide polymorphisms (SNP) than the conventional network representation. Availability R code implementation of NetSHy is available at https://github.com/thaovu1/NetSHy Supplementary information Supplementary data are available at Bioinformatics online.

Proteomic Networks and Related Genetic Variants Associated with Smoking and Chronic Obstructive Pulmonary Disease

“…Network projection: In addition to a direct subnetwork comparison using the PND6 test statistic, we also investigate the similarities and differences between race-specific subnetworks by projecting a subnetwork derived from one race group onto another and vice versa. Specifically, we impose the subnetwork connectivity from one group onto the proteomic data of the other group to compute NetSHy scores as in [42], referred to as projection scores. We calculate correlations between these scores with each respective phenotype or exposure to statistically compare with the original correlations.…”

“…Details are provided in Supplementary Methods . For each subnetwork, we performed a genome-wide network quantitative trait locus (nQTL) analysis of the 3 inverse-normalized NetSHy scores (NetSHy1, NetSHy2, NetSHy3) assuming an additive model for genotype [42]. We regressed the NetSHy scores on each genetic variant separately adjusting for covariates depending on the phenotype used to generate the sub-network.…”

A Generalized Higher-order Correlation Analysis Framework for Multi-Omics Network Inference

“…Then an adjacency matrix between selected features is constructed to identify the inter-molecule relationships and collapse all higher/lower-order correlations into the two-dimensional space. Afterward, a network pruning algorithm is implemented to the adjacency matrix with the PageRank algorithm [30] NetSHy summarization score [31] to reduce the size of the network and include only the most relevant molecular features, yielding the final multi-omics network. Details of the pipeline are described below…”

“…However, even though the adjacency matrix is sparse, it may still contain features/nodes that are less associated with other features/phenotypes. Therefore, we prune the global network with the PageRank algorithm [39] and the NetSHy network summarization score [31]. The original PageRank algorithm is widely used to rank web pages according to their importance.…”

SmCCNet 2.0: A Comprehensive Tool for Multi-omics Network Inference with Shiny Visualization

“…The objective of Step IV is to prune the network by removing features (nodes) that have no/little contribution to the subnetwork using a network summarization score of Principal Component Analysis (PCA) (Abdi and Williams, 2010) or network summarization via a hybrid approach leveraging topological properties (NetSHy) (Vu et al, 2023) to produce a densely connected pruned subnetwork that maintains a high summarization correlation with respect to the phenotype. Initially, the network features are ranked based on their PageRank scores (Page et al, 1998).…”