Tensor Decomposition Based on Global Features and Sparse Structure for Analyzing Cancer Multiomics Data

Background: There are correlations between the multiple types of data stored in the tensor space. The matrix formed by the data in the high-dimensional space is of low rank. Therefore, the potential association between genes and cancers can be explored in low-rank space. Tensor robust principal component analysis (TRPCA) is used to extract information by obtaining coefficient tensors with low-rank representation. In practical applications, global features and sparse structure are ig-nored, which leads to incomplete analysis. Objective: This paper proposes an adaptive reweighted TRPCA method (ARTRPCA) to explore cancer subtypes and identify conjoint abnormally expressed genes (CAEGs). Methods: ARTRCA analyzes data based on adaptive learning of primary information. Meanwhile, the weighting scheme based on singular value updates is used to learn global features in low-rank space. The reweighted l₁ algorithm is based on prior knowledge, which is used to learn about sparse structures. Moreover, the sparsity threshold of Gaussian entries has been increased to reduce the in-fluence of outliers. Results: In the experiment of sample clustering, ARTRPCA has obtained promising experimental results. The identified CAEGs are pathogenic genes of various cancers or are highly expressed in specific cancers. Conclusion: The ATRPCA method has shown excellent application prospects in cancer multiomics data.