GSTRPCA: irregular tensor singular value decomposition for single-cell multi-omics data clustering

Single-cell multi-omics refers to the various types of biological data at the single-cell level. These data have enabled insight and resolution to cellular phenotypes, biological processes, and developmental stages. Current advances hold high potential for breakthroughs by integrating multiple different omics layers. However, singlecell multi-omics data usually have different feature dimensions and direct or indirect relationships. How to keep the data structure of these different data and extract hidden relationships is a major challenge for omics data integration, and effective integration models are urgently needed. In this paper, we propose an irregular tensor decomposition model (GSTRPCA) based on tensor robust principal component analysis (TRPCA). We developed a weighted threshold model for the decomposition of irregular tensor data by combining low-rank and sparsity constraints, which requires that the low-dimensional embeddings of the data remain lowrank and sparse. The major advantage of the GSTRPCA algorithm is its ability to keep the original data structure and explore hidden related features among omics data. For GSTRPCA, we also designed an effective algorithm that theoretically guarantees global convergence for the tensor decomposition. The computational experiments on irregular tensor datasets demonstrate that GSTRPCA significantly outperformed the state-of-the-art methods and hence confirm the superiority of GSTRPCA in clustering single-cell multiomics data. To our knowledge, this is the first tensor decomposition method for irregular tensor data to keep the data structure and hence improve the clustering performance for single-cell multi-omics data. GSTRPCA is a Matlabbased algorithm, and the code is available from https://github.com/GGL-B/GSTRPCA.