报告人: 吴 钢 （中国矿业大学）

日  期: 2019年7月4日

时  间: 15:00

地  点: 理科楼 LD202

摘  要: Canonical correlation analysis (CCA) is a data driven method that has been successfully used in data analysis. Standard CCA extracts meaningful information from a pair of data sets by seeking pairs of linear combinations from two sets of variables with maximum pairwise correlation. Mathematically, CCA resolves to solving large scale generalized eigenvalue problems. However, as the dimension of the data sets is often much large than the number of samples, CCA often suffers from the small sample size (SSS) problem. In order to overcome this difficulty, regularized technique is often utilized in CCA, but the optimal regularized parameter is difficult to choose in advance. As an alternative, we propose an Exponential Canonical Correlation Analysis (ECCA) based on the matrix exponential function. ECCA is parameter free and can overcome the SSS problem intrinsically. The relationship between the regular CCA method and the ECCA method is established. However, the cost of ECCA is very large for practical problems. Based on the randomized singular value decomposition (RSVD) and the ECCA method, we then propose a Random Exponential Canonical Correlation Analysis (RECCA) for data analysis and dimensionality reduction, and the computational overhead can be reduced substantially. Theoretical results are given to show the rationality and the stability of RECCA. Numerical experiments demonstrate the superiority of the proposed algorithms over some popular CCA algorithms on some real-world and synthetic data sets.

报告人简介：吴钢，博士、中国矿业大学数学学科教授、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、数据挖掘与机器学习等。1994年9月-1998年7月就读于山东大学数学与系统科学学院计算数学及其应用软件专业，获理学学士学位；1998年9月-2001年7月就读于大连理工大学应用数学系，获理学硕士学位；2001年9月-2004年7月就读于复旦大学数学研究所，获理学博士学位。先后主持国家自然科学基金3项、江苏省省自然科学基金项目2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, Journal of Scientific Computing, Applied Numerical Mathematics, Data Mining and Knowledge Discovery, ACM Transactions on Information Systems等发表学术论文多篇。

更详细信息见吴钢教授主页http://www.escience.cn/people/gangwu/index.html

学院联系人:李寒宇

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