江苏省应用数学（中国矿业大学）中心系列学术报告
报告题目：Irregular tensor singular value decomposition for single-cell multi-omics data clustering
报告人：崔鲁宾 教授 河南师范大学数学与统计学院
报告时间：2025年5月9日（周五）上午 9:00-10:00
报告地点：数学学院 A321
报告人简介：崔鲁宾，河南师范大学数学与统计学院教授，硕士生导师，信息与计算科学系主任，香港大学、香港浸会大学访问学者，主持完成国家自然科学基金项目3项，河南省教育厅重点项目2项，横向项目2项，曾在SIAM J. Matrix Anal. Appl.，Numer. Lin. Alg. Appl., Front. Math. China, JOTA等SCI期刊发表论文10多篇，其中ESI高被引论文3篇。曾获河南省优秀硕士论文指导教师、河南省自然科学学术论文一等奖、二等奖各1项、指导学生参加“华为杯”中国研究生数学建模竞赛获得国家一等奖3项等。
报告摘要：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, single-cell 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 low rank 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.