View-Specific Optimal Rank Based Joint Subspace Clustering for Multi-Omics Cancer Subtyping

Data from multiple omics modalities such as genomic, proteomic and transcriptomic are often used simultaneously to leverage consensus and complementary information across the modalities. It facilitates better diagnosis and prognosis of the diseases. However, different modalities or views may have a high degree of heterogeneity in the dimensionality, scale and variance, and are often perturbed with varying amount of noise. The existing methods of clustering multi-omics data typically form a joint subspace from a common low-rank representation of the views, and perform subspace clustering. These approaches, however, fail to capture the heterogeneity in rank of individual views. In this regard, a novel approach is proposed to perform clustering on multi-view data, considering view-specific optimal rank for efficient low-rank representation. A theoretical bound is established on the rank of the shifted Laplacian of each view, in terms of the number of components of the similarity graph. An entropy based regularization is introduced to learn the weight, which depends on the prior relevance of each view. A new quantitative index is proposed to compute the relevance of each view. It not only considers the clustering ability of the given view, but also takes into account the amount of noise present in the view, which is expressed in terms of rank of the view. Rigorous experimentation on multi-omics data sets obtained from The Cancer Genomic Atlas (TCGA) shows that the proposed method performs significantly better than the state-of-the-art methods.