报 告 人：徐玮玮 教授

报告题目：Efficient Linear Discriminant Analysis based on Randomized Low-Rank Approaches

报告时间：2025年4月15日（周二）上午10:00—11:00

报告地点：腾讯会议 会议号：524-340-087

主办单位：数学与统计学院、数学研究院、科学技术研究院

报告人简介：

      徐玮玮，现为南京信息工程大学教授，博士生导师。研究方向为矩阵计算理论与技术应用。学士和博士毕业于华南师范大学，博士毕业后进入中科院数学与系统科学研究院博士后流动站工作。在National Science Review, Mathematics of Computation, SIAM J. Optim., SIAM J. Matrix Anal. Appl., IEEE Trasctions on Neural Networks and Learning Systems等著名杂志上发表学术论文40余篇; 主持国家和省部级基金5项；2020年入选江苏省“青蓝工程”优秀骨干教师。2022年受聘国家天元数学西北中心“天元学者”。2022年获得粤港澳大湾区(黄埔)国际算法算例大赛冠军。

报告摘要：

      Linear Discriminant Analysis (LDA) faces challenges in practical applications due to the small sample size (SSS) problem and high computational costs. Various solutions have been proposed to address the SSS problem in both ratio trace LDA and trace ratio LDA. However, the iterative processing of large matrices often makes the computation process cumbersome. To address this issue, for trace ratio LDA, we propose a novel random method that extracts orthogonal bases from matrices, allowing computations with smaller-sized matrices. This significantly reduces computational time without compromising accuracy. For ratio trace LDA, we introduce a fast generalized singular value decomposition (GSVD) algorithm, which demonstrates superior speed compared to MATLAB's built-in GSVD algorithm in experiments. By integrating this new GSVD algorithm into ratio trace LDA, we propose FGSVD-LDA, which exhibits low computational complexity and good classification performance. Experimental results show that both methods effectively achieve dimensionality reduction and deliver satisfactory classification accuracy.