A Tensor Method Based on Enhanced Tensor Nuclear Norm and Hypergraph Laplacian Regularization for Pan-Cancer Omics Data Analysis.

As a powerful data representation technique, tensor robust principal component analysis (TRPCA) has been widely used for clustering and feature selection tasks. However, it ignores the significant difference in singular values of tensor data and the manifold information contained in different views, thereby causing serious degradation of conventional TRPCA performance. In this paper, a novel tensor method based on enhanced tensor nuclear norm and hypergraph Laplacian regularization (ETHLR) is developed to address the above problem. ETHLR can jointly learn the prior knowledge of singular values and high-order manifold structures in the unified tensor space and the view-specific feature spaces, respectively. Specifically, the enhanced tensor nuclear norm, namely, the weighted tensor Schatten p-norm, is used to shrink the singular values by fully considering the salient difference information of singular values and the complementary information embedded in the tensor space; the hypergraph Laplacian constraint helps encode high-order geometric structures among multiple samples in the nonlinear view-specific feature space. Furthermore, we employ inexact augmented Lagrange multipliers (ALM) to optimize the ETHLR method. Numerous experiments on pan-cancer omics data show that the superiority of ETHLR over several state-of-the-art competitors.