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

Area of Science:

• Genomics
• Bioinformatics
• Data Science

Background:

• Tensor Robust Principal Component Analysis (TRPCA) shows promise in genomics data analysis.
• Existing TRPCA models using tensor singular value decomposition (SVD) struggle to fully extract low-rank structures, leading to suboptimal results.
• The standard tensor nuclear norm (TNN) treats all singular values equally, failing to preserve crucial information.

Purpose of the Study:

• To propose a novel Tensor Nuclear Norm (TNN) for preserving heterogeneous low-rank structures in genomics data.
• To extend this novel TNN to the TRPCA model for improved data analysis.
• To effectively learn low-rank structural information from the core tensor and capture gene-cancer associations.

Main Methods:

• Development of a novel Tensor Nuclear Norm (TNN) that accounts for differing singular value importance.
• Extension of TRPCA by incorporating the new TNN to better preserve heterogeneous low-rank information.
• Utilization of a [Formula: see text]-shrinkage generalized threshold function to maintain low-rank properties of significant singular values.
• Solving the optimization problem using the Alternating Direction Method of Multipliers (ADMM) algorithm.

Main Results:

• The proposed TRPCA model demonstrates superior performance in extracting low-rank structures compared to existing methods.
• Experiments on TCGA data for clustering and feature selection show the model's effectiveness.
• The novel TNN successfully preserves heterogeneous structures within the low-rank information.

Conclusions:

• The enhanced TRPCA model with the novel TNN offers a more promising approach for genomics data analysis.
• This method effectively captures gene-cancer associations by preserving critical low-rank information.
• The proposed approach outperforms current state-of-the-art tensor decomposition techniques.