Tensor decomposition based on the potential low-rank and p -shrinkage generalized threshold algorithm for analyzing cancer multiomics data

Tensor Robust Principal Component Analysis (TRPCA) has achieved promising results in the analysis of genomics data. However, the TRPCA model under the existing tensor singular value decomposition (t-SVD) framework insufficiently extracts the potential low-rank structure of the data, resulting in suboptimal restored components. Simultaneously, the tensor nuclear norm (TNN) defined based on t-SVD uses the same standard to handle various singular values. TNN ignores the difference of singular values, leading to the failure of the main information that needs to be well preserved. To preserve the heterogeneous structure in the low-rank information, we propose a novel TNN and extend it to the TRPCA model. Potential low-rank space may contain important information. We learn the low-rank structural information from the core tensor. The singular value space contains the association information between genes and cancers. The p-shrinkage generalized threshold function is utilized to preserve the low-rank properties of larger singular values. The optimization problem is solved by the alternating direction method of the multiplier (ADMM) algorithm. Clustering and feature selection experiments are performed on the TCGA data set. The experimental results show that the proposed model is more promising than other state-of-the-art tensor decomposition methods.