题  目:  A Framework on Fast Implementation of Matrix Exponential Discriminant Methods for High Dimensionality Reduction

报告人：吴钢  教授

 摘  要: Recently, some matrix exponential-based discriminant methods were proposed for high dimensionality reduction.
It has been shown that they have more discriminant power than some conventional methods.
However, we have to compute and form two large scale matrix exponentials explicitly, as well as to solve a large scale eigenvalue problem, which are the bottleneck in these methods. We propose a framework on fast implementation of general matrix exponential-based discriminant methods. The key is to equivalently transform large matrix computation problems of size $d$ into much small ones of size $n$, where $d$ is the dimensionality of the data and $n$ is the number of samples, with $d\gg n$ in practice.
As the transformation is mathematically equivalent, there is no recognition rate lost in the accelerated algorithms, relative to their original counterpart.
Stability analysis is given to show why the matrix exponential-based discriminant methods are stable to perturbations.
Numerical experiments show the efficiency of the proposed algorithms, and illustrate the superiority of them over many state-of-the-art algorithms for high dimensionality reduction.

时  间：2018年6月8日 下午1:30-3:30

地  点：教学楼411

报告人简介：中国矿业大学教授、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，江苏省数学会计算数学分会副理事长。 研究方向：大规模科学与工程计算、数值代数、统计计算与数据挖掘。 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，师从贾仲孝教授，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，师从曹志浩教授，获理学博士学位。 主持国家、省自然科学基金多项，在国际知名杂志，如：SIAM Journal on Matrix Analysis and Applications, SIAM Journal on Scientific Computing, SIAM Journal on Numerical Analysis, IMA Journal of Numerical Analysis, Pattern Recognition, Journal of Scientific Computing, Data Mining and Knowledge Discovery, ACM Transactions on Information Systems 上发表学术论文多篇。

邀请人: 陶敏 老师