vWCluster: A Network Based Clustering of Multi-omics Breast Cancer Data Based on Vector-Valued Optimal Transport

In this paper, we present a network-based clustering method based on the vector-valued Wasserstein distance derived from optimal mass transport (OMT) theory. This distance allows for the natural integration of multi-layer representations of data in a given network from which one derives clusters via a hierarchical clustering approach. In this study, we applied the methodology, called vector Wasserstein clustering (vW-cluster), to multi-omics data from the two largest breast cancer studies. The resultant clusters showed significantly different survival rates in Kaplan-Meier analysis in both datasets. CIBERSORT scores were compared among the identified clusters. Out of the 22 CIBERSORT immune cell types, 9 were commonly significantly different in both datasets, suggesting the difference of tumor immune microenvironment in the cluster. vWCluster can aggregate multi-omics data represented as a vectorial form in a network with multiple layers, taking into account the concordant effect of heterogeneous data, and further identify subtypes of tumors with different survival rates.