Bayesian Multi-View Clustering given complex inter-view structure [version 2; peer review: 2 approved]

Multi-view datasets are becoming increasingly prevalent. These datasets consist of different modalities that provide complementary characterizations of the same underlying system. They can include heterogeneous types of information with complex relationships, varying degrees of missingness, and assorted sample sizes, as is often the case in multi-omic biological studies. Clustering multi-view data allows us to leverage different modalities to infer underlying systematic structure, but most existing approaches are limited to contexts in which entities are the same across views or have clear one-to-one relationships across data types with a common sample size. Many methods also make strong assumptions about the similarities of clusterings across views. We propose a Bayesian multi-view clustering approach (BMVC) which can handle the realities of multi-view datasets that often have complex relationships and diverse structure. BMVC incorporates known and complex many-to-many relationships between entities via a probabilistic graphical model that enables the joint inference of clusterings specific to each view, but where each view informs the others. Additionally, BMVC estimates the strength of the relationships between each pair of views, thus moderating the degree to which it imposes dependence constraints. We benchmarked BMVC on simulated data to show that it accurately estimates varying degrees of inter-view dependence when inter-view relationships are not limited to one-to-one correspondence. Next, we demonstrated its ability to capture visually interpretable inter-view structure in a public health survey of individuals and households in Puerto Rico following Hurricane Maria. Finally, we showed that BMVC clusters integrate the complex relationships between multi-omic profiles of breast cancer patient data, improving the biological homogeneity of clusters and elucidating hypotheses for functional biological mechanisms. We found that BMVC leverages complex inter-view structure to produce higher quality clusters than those generated by standard approaches. We also showed that BMVC is a valuable tool for real-world discovery and hypothesis generation.