报告题目：A Randomized Algorithm for Trace-ratio Problem of High-dimensional Tensor Data
时 间：2025年12月11日（星期四）16：00
地 点：科研楼18号楼1102
主 办：数学与统计学院、分析数学及应用教育部重点实验室、福建省分析数学及应用重点实验室、福建省应用数学中心（福建师范大学）、福建师范大学数学研究中心
参加对象：感兴趣的老师和研究生
报告摘要：Trace-ratio optimization of high-dimensional tensor data is widely used in many fields such as machine learning, signal processing and pattern recognition. The goal is to map original data from a high-dimensional space to a low-dimensional space on the premise of preserving the essential information of the original data as much as possible. Available multilinear discriminant analysis method may encounter limitations such as the curse of dimensionality and interference from redundant features when dealing with high-dimensional tensor data, which leads to suboptimal performance. To the best of our knowledge, there is no closed-form solution to solve the tensor trace-ratio problem, and the existing methods generally use inner-outer iterative algorithms for this problem. Specifically, for large-scale high-dimensional data, we have to face with the challenges of dimensional disaster, time-consuming, insufficient memory space, and so on. In order to overcome these difficulties, we give a closed-form solution in this work, and the proposed randomized algorithm can reduce the computational complexities significantly. Theoretical error bound is established to guarantee the effectiveness. Moreover, a sparse tensor discriminant analysis method is proposed to achieve feature selection and dimensionality reduction. This method can identify key discriminative features from high-dimensional data and suppress redundant information. Comprehensive numerical experiments are performed on some real-world data sets, to verify the feasibility and efficiency of the proposed methods.
报告人简介：吴钢，博士、中国矿业大学数学学院教授、博士生导师；江苏省“333 工程” 中青年科学技术带头人，江苏省“青蓝工程”中青年学术带头人；江苏省计算数学学会副理事长。主要研究方向：大规模科学与工程计算、数值代数、机器学习与模式识别、大数据与人工智能中的快速算法等。目前已主持国家自然科学基金项目4项、省自然科学基金项目2项、市厅重点研发计划1项，在国际知名杂志，如：SIAM Journal on Numerical Analysis, SIAM Journal on Matrix Analysis and Applications, SIAM Journal on Scientific Computing, IMA Journal of Numerical Analysis, IEEE Transactions on Knowledge and Data Engineering, Pattern Recognition, Machine Learning, ACM Transactions on Information Systems 等期刊发表学术论文60余篇。