报告题目：New algorithms for trace-ratio problem with application to high-dimension and large-sample data dimensionality reduction
摘要：Learning large-scale data sets with high dimensionality is a main concern in research areas including machine learning, visual recognition, information retrieval, to name a few. In many practical uses such as images, video, audio, and text processing, we have to face with high-dimension and large-sample data problems. The trace-ratio problem is a key problem for feature extraction and dimensionality reduction to circumvent the high dimensional space. However, it has been long believed that this problem has no closed-form solution, and one has to solve it by using some inner-outer iterative algorithms that are very time consuming. Therefore, efficient algorithms for high-dimension and large-sample trace-ratio problems are still lacking, especially for dense data problems. In this work, we present a closed-form solution for the trace-ratio problem, and propose two algorithms to solve it. Based on the formula and the randomized singular value decomposition, we first propose a randomized algorithm for solving high-dimension and large-sample dense trace-ratio problems. For high-dimension and large-sample sparse trace-ratio problems, we then propose an algorithm based on the closed-form solution and solving some consistent under-determined linear systems. Theoretical results are established to show the rationality and efficiency of the proposed methods. Numerical experiments are performed on some real-world data sets, which illustrate the superiority of the proposed algorithms over many state-of-the-art algorithms for high-dimension and large-sample dimensionality reduction problems.
报告时间：2021/12/02 09:00-10:00 (GMT+08:00) 中国标准时间-北京
专家简介：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，现任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、机器学习与数据挖掘等。先后主持国家自然科学基金项目、江苏省省自然科学基金项目多项，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, Pattern Recognition, Machine Learning等期刊发表学术论文多篇。