Bayesian evolutionary hypergraph learning for predicting cancer clinical outcomes

HC-HDSD: A method of hypergraph construction and high-density subgraph detection for inferring high-order epistatic interactions

Detecting epistatic interactions, or nonlinear interactive effects of Single Nucleotide Polymorphisms (SNPs), has gained increasing attention in explaining the "missing heritability" of complex diseases. Though much work has been done in mapping SNPs underlying diseases, most of them constrain to 2-order epistatic interactions. In this paper, a method of hypergraph construction and high-density subgraph detection, named HC-HDSD, is proposed for detecting high-order epistatic interactions. The hypergraph is constructed by low-order epistatic interactions that identified using the normalized co-information measure and the exhaustive search. The hypergraph consists of two types of vertices: real ones representing main effects of SNPs and virtual ones denoting interactive effects of epistatic interactions. Then, both maximal clique centrality algorithm and near-clique mining algorithm are employed to detect high-density subgraphs from the constructed hypergraph. These high-density subgraphs are inferred as high-order epistatic interactions in the HC-HDSD. Experiments are performed on several simulation data sets, results of which show that HC-HDSD is promising in inferring high-order epistatic interactions while substantially reducing the computation cost. In addition, the application of HC-HDSD on a real Age-related Macular Degeneration (AMD) data set provides several new clues for the exploration of causative factors of AMD.

The Evolution of Hyperedge Cardinalities and Bose-Einstein Condensation in Hypernetworks

To depict the complex relationship among nodes and the evolving process of a complex system, a Bose-Einstein hypernetwork is proposed in this paper. Based on two basic evolutionary mechanisms, growth and preference jumping, the distribution of hyperedge cardinalities is studied. The Poisson process theory is used to describe the arrival process of new node batches. And, by using the Poisson process theory and a continuity technique, the hypernetwork is analyzed and the characteristic equation of hyperedge cardinalities is obtained. Additionally, an analytical expression for the stationary average hyperedge cardinality distribution is derived by employing the characteristic equation, from which Bose-Einstein condensation in the hypernetwork is obtained. The theoretical analyses in this paper agree with the conducted numerical simulations. This is the first study on the hyperedge cardinality in hypernetworks, where Bose-Einstein condensation can be regarded as a special case of hypernetworks. Moreover, a condensation degree is also discussed with which Bose-Einstein condensation can be classified.

Filtered selection coupled with support vector machines generate a functionally relevant prediction model for colorectal cancer

Purpose

There has been considerable interest in using whole-genome expression profiles for the classification of colorectal cancer (CRC). The selection of important features is a crucial step before training a classifier.

Methods

In this study, we built a model that uses support vector machine (SVM) to classify cancer and normal samples using Affymetrix exon microarray data obtained from 90 samples of 48 patients diagnosed with CRC. From the 22,011 genes, we selected the 20, 30, 50, 100, 200, 300, and 500 genes most relevant to CRC using the minimum-redundancy–maximum-relevance (mRMR) technique. With these gene sets, an SVM model was designed using four different kernel types (linear, polynomial, radial basis function [RBF], and sigmoid).

Results

The best model, which used 30 genes and RBF kernel, outperformed other combinations; it had an accuracy of 84% for both ten fold and leave-one-out cross validations in discriminating the cancer samples from the normal samples. With this 30 genes set from mRMR, six classifiers were trained using random forest (RF), Bayes net (BN), multilayer perceptron (MLP), naïve Bayes (NB), reduced error pruning tree (REPT), and SVM. Two hybrids, mRMR + SVM and mRMR + BN, were the best models when tested on other datasets, and they achieved a prediction accuracy of 95.27% and 91.99%, respectively, compared to other mRMR hybrid models (mRMR + RF, mRMR + NB, mRMR + REPT, and mRMR + MLP). Ingenuity pathway analysis was used to analyze the functions of the 30 genes selected for this model and their potential association with CRC: CDH3, CEACAM7, CLDN1, IL8, IL6R, MMP1, MMP7, and TGFB1 were predicted to be CRC biomarkers.

Conclusion

This model could be used to further develop a diagnostic tool for predicting CRC based on gene expression data from patient samples.

3-way networks: application of hypergraphs for modelling increased complexity in comparative genomics

We present and develop the theory of 3-way networks, a type of hypergraph in which each edge models relationships between triplets of objects as opposed to pairs of objects as done by standard network models. We explore approaches of how to prune these 3-way networks, illustrate their utility in comparative genomics and demonstrate how they find relationships which would be missed by standard 2-way network models using a phylogenomic dataset of 211 bacterial genomes.

Genomes contain the information underlying the molecular functions of an organism. One way to compare the entire genomes of different organisms is to compare their gene-family content profiles which is effectively a comparison of their functional potential. Standard networks, when used to model phylogenomic similarities, are not capable of capturing some of the underlying complexity of the relationships between genomes. In order to address this, we have developed a new three-way similarity metric and constructed three-way networks modelling the relationships between 211 bacterial genomes. We find that such three-way networks find cross-species genomic similarities that would have been otherwise missed by simpler models such as standard networks.