Trace optimization and eigenvector-dependent nonlinear eigenvalue problems in data science

Abstract

Some recent applications of multivariate statistical analysis in data science need to optimize certain trace-related objective functions over the orthogonal constraints. In this talk, we shall first present some recent applications in data science and show that solving the optimization problems can be converted to eigenvector-dependent eigenvalue problems (NEPv) for which the self-consistent filed (SCF) iteration can be effectively applied. We then discuss recent developments of the general SCF on the local convergence rate and the level-shifted technique.

Speaker

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。主持多项国家自科项目，参与国家自然科学基金重大研究计划。在《Math Program》《Math. Comput.》《Numer. Math.》《IEEE TPAMI》以及SIAM期刊系列等发表六十多篇学术论文。