报告人：张振跃教授  浙江大学

 报告题目：Low Rank Matrix Approximation Preserving Nonlinear Manifold Structures

  时    间：2017年1月8 日(星期日) 19:30 ~21:00

  地    点：福州大学数计学院4号楼229报告厅   

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.

  报告人简介：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的模型与算法的理论分析与计算。先后在在国际著名学术刊物SIAM Review、SIAM J. Scientific Computing、SIAM J. Matrix Analysis and Application、SIAM J Numerical Analysis、 IEEE TPAMI 、Patten Recognition,以及NIPS、CVPR等会议上发表80余篇研究论文，在相关研究中取得了受到许多国际关注的系统性研究成果。他是第一位在国际应用数学最顶尖的刊物SIAMReview上发表研究论文的国内大陆学者。部分数值代数工作被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 》等重要的国际数值计算专著所引用。其关于非线性降维算法的工作，多年来一直列SIAM J. Scientific Computing 10年高引用率第4、5位。在国际机器学习领域中被广泛应用的scikit-learn 中收录的8个关于流形学习的经典算法中，有两个属于张教授及其合作者。张振跃教授现任浙江省数学会理事，《计算数学》和《高校计算数学》编委。