主讲人：徐立伟

讲座时间：2024年5月23日（星期四）9：00

讲座地点：1212

讲座对象：全校师生

主要内容：

In this talk, we first introduce a stochastic Gauss-Newton (SGN) algorithm to study the online principal component analysis (OPCA) problem, which is formulated by using the symmetric low-rank product model for dominant eigenspace calculation. Compared with existing OPCA solvers, SGN is of improved robustness with respect to the varying input data and algorithm parameters. In addition, turning to an evaluation of data stream based on approximated objective functions, we develop a new adaptive stepsize strategy for SGN which requires no priori knowledge of the input data, and numerically illustrate its comparable performance with SGN adopting the manaully-tuned diminishing stepsize. Without assuming the eigengap to be positive, we also establish the global and optimal convergence rate of SGN with the specified stepsize using the diffusion approximation theory.

Then, we present an orthonormalization- and inversion-free incremental PCA scheme (Domino). The Domino is shown to achieve the computational speed-up, and own the ability of automatic correction on the numerical rank. It also maintains the advantage of Krasulina's method, e.g., variance reduction on low-rank data. Moreover, both of the asymptotic and non-asymptotic convergence guarantees are established for the proposed algorithm.

专家简介：

徐立伟,电子科技大学数学科学学院教授、院长、博士生导师。主要研究方向为波动方程与流体力学方程有限元与边界元方法，在SIAM Nume. Anal.,Numer.Math., SIAM Sci.Comp., J.Comp.Phys.等应用和计算数学学术刊物上发表论文50余篇。现担任电子科技大学数学科学学院院长、国家基金委评审专家、教育部高等学校数学类专业教学指导委员会委员、中国工业与应用数学学会理事、中国数学会计算数学分会常务理事兼副秘书长、《计算数学》编委等。