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(shù)學(xué)與統(tǒng)計學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報告人簡介：

      徐瑋瑋，現(xiàn)為南京信息工程大學(xué)教授，博士生導(dǎo)師。研究方向為矩陣計算理論與技術(shù)應(yīng)用。學(xué)士和博士畢業(yè)于華南師范大學(xué)，博士畢業(yè)后進入中科院數(shù)學(xué)與系統(tǒng)科學(xué)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(fā)表學(xué)術(shù)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(yōu)秀骨干教師。2022年受聘國家天元數(shù)學(xué)西北中心“天元學(xué)者”。2022年獲得粵港澳大灣區(qū)(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.