A randomized exponential canonical correlation analysis method for data analysis and dimensionality reduction
- A+
：吴钢（中国矿业大学）
：2022-04-23 10:00
：腾讯会议ID：298384882（无密码）
报告人：吴钢（中国矿业大学）
时 间：4月23日上午10:00
地 点：腾讯会议ID：298384882（无密码）
内容摘要:
Canonical correlation analysis (CCA) is a famous data analysis method that has been successfully used in many areas. CCA extracts meaningful information from a pair of data sets, by seeking pairs of linear combinations from two sets of variables with maximum correlation. Mathematically, CCA resorts to solving a large-scale generalized eigenvalue problem. However, as the dimension of the data sets is much larger than the number of samples, CCA may suffer from the small-sample-size (SSS) problem and the over-fitting problem. In order to overcome these difficulties, the regularized technique is often applied, but it is difficult to choose the optimal parameter in advance. In this work, we propose an Exponential Canonical Correlation Analysis (ECCA) method based on matrix exponential, which is parameter-free and can overcome the over-fitting and the SSS problems fundamentally. However, the computational overhead of the ECCA method is very high in practice. Based on the randomized singular value decomposition (RSVD), we then propose a Randomized Exponential Canonical Correlation Analysis (RECCA) method for data analysis and dimensionality reduction. Theoretical results are given to show the rationality of this randomized method, and establish the relationship between RECCA and ECCA. Numerical experiments are performed on some real-world, high-dimensional and large-sample data sets, which illustrate the superiority of the proposed algorithms over many state-of-the-art CCA algorithms.
个人简介：
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 Scientific Computing, SIAM Journal on Matrix Analysis and Applications, IMA Journal of Numerical Analysis, Pattern Recognition, Machine Learning 等期刊发表学术论文多篇。
联系人：白正简
