题目： A Self-Consistent-Field Iteration for MAXBET With an Application to Multi-view Feature Extraction
报告人：张雷洪 教授单位： 苏州大学 数学科学学院
时 间：2021年10月5日（周二）下午 15:00-16:00
腾讯会议 ID：310 252 644
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报告内容简介：
As an extension of the traditional principal component analysis, the multi-view canonical correlation analysis (MCCA) aims at reducing $m$ high dimensional random variables $s_i\in R^{n_i}~(i=1,2,\ldots,m)$ by proper projection atrices $X_i\in R^{n_i\times \ell}$ so that the $m$ reduced ones $y_i=X_i^{T}s_i\in R^{\ell}$ have the `maximal correlation'. Various measures of the correlation for $y_i~(i=1,2,\ldots,m)$ in MCCA have been proposed. One of the earliest criteria is the sum of all traces of pair-wise correlation matrices between $y_i$ and $y_j$ subject to the orthogonality constraints on X_i,~i=1,2,\ldots,m$. The resulting problem is to maximize a homogeneous quadratic function over the product of Stiefel manifolds and is referred to as the MAXBET problem. In this talk, the problem is first reformulated as a coupled nonlinear eigenvalue problem with eigenvector dependency (NEPv) and then solved by a novel self-consistent-field (SCF) iteration. Global and local convergence of the SCF iteration are studied and proving computational techniques in the standard eigenvalue problem are incorporated to yield more practical implementations. Besides the preliminary numerical evaluations on various types of synthetic problems, the efficiency of the SCF iteration is also demonstrated in an application to multi-view feature extraction for unsupervised learning.
报告人简介
张雷洪于2008年博士毕业于香港浸会大学，现为苏州大学数学科学学院特聘教授、博士生导师。长期从事最优化理论与计算、数值线性代数、模式识别、数据挖掘等领域的研究。主持国家自然科学基金青年/面上项目，参与国家自然科学基金重大研究计划。在数值代数、最优化及数据科学相关的研究上，发表五十多篇学术论文。其中有发表于计算数学和机器学习领域权威期刊，如 Math. Comput.、Numer. Math.、IEEE TPMAI, 以及十余篇SIAM期刊系列等。曾获第四届中国数学会计算数学分会颁发的“应用数值代数奖’’、上海财经大学第四届学术奖、2018和2019年两届世界华人数学家联盟最佳论文奖（若琳奖），及2019年上海市自然科学三等奖（第一完成人）等。现为学术杂志《Operators and Matrices》和《Numerical Algebra, Control and Optimization》的编委。