報 告 人：徐瑋瑋 教授

報告題目：Efficient Linear Discriminant Analysis based on Randomized Low-Rank Approaches

報告時間：2025年4月15日（周二）上午10:00—11:00

報告地點：騰訊會議 會議號：524-340-087

主辦單位：數學與統計學院、數學研究院、科學技術研究院

報告人簡介：

      徐瑋瑋，現為南京信息工程大學教授，博士生導師。研究方向為矩陣計算理論與技術應用。學士和博士畢業于華南師范大學，博士畢業后進入中科院數學與系統科學研究院博士后流動站工作。在National Science Review, Mathematics of Computation, SIAM J. Optim., SIAM J. Matrix Anal. Appl., IEEE Trasctions on Neural Networks and Learning Systems等著名雜志上發表學術論文40余篇; 主持國家和省部級基金5項；2020年入選江蘇省“青藍工程”優秀骨干教師。2022年受聘國家天元數學西北中心“天元學者”。2022年獲得粵港澳大灣區(黃埔)國際算法算例大賽冠軍。

報告摘要：

      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.