时间：2017年1月8日（周日）09：00 - 11：00
地点：旗山校区理工北楼601报告厅
主讲：浙江大学 张振跃教授
主办：数学与计算机科学学院、福建省分析数学及应用重点实验室、数学研究中心
专家简介：张振跃，浙江大学数学系二级教授、博士生导师，浙江大学信息数学研究所所长。2013年获浙江大学心平教学杰出贡献奖，2014年获国务院政府津贴。1989年7月获复旦大学理学博士学位后，进入浙江大学数学系任教。主要从事数值代数、科学计算、大数据分析等研究领域模型与算法的理论分析与计算。先后在国际著名学术刊物和国际会议上发表80余篇研究论文，第一位在国际应用数学最顶尖的刊物《SIAMReview》发表研究论文的中国大陆学者。研究成果被G. Golub教授和VanLoan教授的专著《Matrix Computations》（第三版）、B.N.Parlett教授的专著《The Symmetric Eigenvalue Problem》和G. Stewart教授与孙继广教授的专著《Matrix Perturbation Theory 》引用。多年来一直列SIAM J. Scientific Computing 10年高引用率第4、5位。浙江省数学会理事，《计算数学》与《高校计算数学》编委。
报告摘要：Low-rank approximation is basically a linear approach if the technique is used for low-dimensional projection in applications. It may be a challenge problem to preserve nonlinear structures of nonlinear manifolds when we consider a linear projection on a nonlinear manifold. In this talk, we will show a new model of low-rank matrix factorization for linearly projecting a nonlinear manifold, while preserving the manifold structure. The new method incorporates manifold regularization to the matrix low-rank factorization. It has globally optimal and closed form solutions, similar with the classical SVD that may distort the nonlinear structure. A direct algorithm (for data with small number of points) and an alternate iterative algorithm with inexact inner iteration (for large scale data) are proposed to solve the new model. We will give an analysis to show the global convergence of the iterative algorithm. Efficiency and precision of the algorithm are demonstrated numerically through applications to six real-world data sets on clustering and classification. Performance comparison with existing algorithms shows the effectiveness of the proposed method for low-rank factorization in general.