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

Area of Science:

• Computational Biology
• Data Science
• Machine Learning

Background:

• Tensor robust principal component analysis (TRPCA) is a key technique for clustering and feature selection.
• Conventional TRPCA methods often overlook crucial tensor data characteristics like singular value differences and manifold information.
• These oversights lead to performance degradation in complex datasets.

Purpose of the Study:

• To develop a novel tensor method, ETHLR, that overcomes the limitations of conventional TRPCA.
• To enhance the performance of tensor-based data analysis by integrating singular value properties and manifold structures.
• To improve clustering and feature selection accuracy in omics data.

Main Methods:

• Introduced an enhanced tensor nuclear norm (weighted tensor Schatten p-norm) to account for singular value differences.
• Incorporated hypergraph Laplacian regularization to capture high-order manifold structures in view-specific feature spaces.
• Utilized inexact augmented Lagrange multipliers (ALM) for efficient optimization of the ETHLR model.

Main Results:

• The proposed ETHLR method demonstrated superior performance compared to existing state-of-the-art methods.
• Experiments on pan-cancer omics data validated the effectiveness of ETHLR in clustering and feature selection.
• ETHLR successfully integrates prior knowledge of singular values and high-order manifold structures.

Conclusions:

• ETHLR offers a significant advancement over traditional TRPCA for data representation tasks.
• The method's ability to leverage both tensor properties and manifold structures enhances analytical power.
• ETHLR shows strong potential for applications in complex biological data analysis.