Integrating multidimensional data for clustering analysis with applications to cancer patient data.

Advances in high-throughput genomic technologies coupled with large-scale studies including The Cancer Genome Atlas (TCGA) project have generated rich resources of diverse types of omics data to better understand cancer etiology and treatment responses. Clustering patients into subtypes with similar disease etiologies and/or treatment responses using multiple omics data types has the potential to improve the precision of clustering than using a single data type. However, in practice, patient clustering is still mostly based on a single type of omics data or ad hoc integration of clustering results from individual data types, leading to potential loss of information. By treating each omics data type as a different informative representation from patients, we propose a novel multi-view spectral clustering framework to integrate different omics data types measured from the same subject. We learn the weight of each data type as well as a similarity measure between patients via a non-convex optimization framework. We solve the proposed non-convex problem iteratively using the ADMM algorithm and show the convergence of the algorithm. The accuracy and robustness of the proposed clustering method is studied both in theory and through various synthetic data. When our method is applied to the TCGA data, the patient clusters inferred by our method show more significant differences in survival times between clusters than those inferred from existing clustering methods.