A novel PSO-based graph-theoretic approach for identifying most relevant and non-redundant gene markers from gene expression data

Cancer is an extremely complex, heterogeneous and mutated genetic disease. Many researchers in molecular genetics have predicted a number of key genes which probably contribute to oncogenesis and potential drug targets for different types of cancer. However, this is still an ongoing process. In this article, not only the gene relevance is considered, but also the redundancy among genes is taken care of. For identifying the non-redundant gene markers from microarray gene expression data, a graph-theoretic approach has been presented. The sample versus gene data presented by microarray data are first converted into a weighted undirected complete feature-graph where the nodes represent the genes having gene's relevance as node weights and the edges are weighted according to the similarity value (correlation) among the genes. Then, the densest subgraph having minimum average edge weight (similarity) and maximum average node weight (relevance) is identified from the original feature-graph. To find the densest subgraph, binary particle swarm optimisation has been applied for minimising the average edge weight and maximising the average node weight through a single objective function. Thus, an optimised reduced subgraph is found which contains a set of selected genes for which average correlation is very less and average gene relevance is very high. The proposed method is compared with sequential forward search, T-test, Rank-sum test, minimum redundancy maximum relevance scheme, correlation-based feature selection, sequential backward elimination and fast correlation-based filter solutions in terms of sensitivity, specificity, accuracy, F-score, area under the receiver operating characteristic curve, average correlation and stability on several real-life data-sets.