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【5月10日】 Minimal Sample Subspace Learning: Theory and Algorithms

来自: 数学与统计学院       作者:   编辑:邱楠       时间:2019-04-30





报告摘要Subspace segmentation or subspace learning is a challenging and complicated task in machine learning. In this talk, we will build a primary frame and solid theoretical bases for the minimal subspace segmentation (MSS) of finite samples. Existence and conditional uniqueness of MSS are discussed with conditions generally satisfied in applications. Utilizing weak prior information of MSS, the minimality inspection of segments is further simplified to the prior detection of partitions. The MSS problem is then modeled as a computable optimization problem via self-expressiveness of samples. A closed form of representation matrices is first given for the self-expressiveness, and the connection of diagonal blocks is then addressed. The MSS model uses a rank restriction on the sum of segment ranks. Theoretically, it can retrieve the minimal sample subspaces that could be heavily intersected. The optimization problem is solved via a basic manifold conjugate gradient algorithm, alternative optimization and hybrid optimization, taking into account of solving both the primal MSS problem and its pseudo-dual problem. The MSS model is further modified for handling noisy data, and solved by an ADMM algorithm. The reported experiments show the strong ability of the MSS method on retrieving minimal sample subspaces that are heavily intersected.



张振跃,男,浙江大学数学学院二级教授,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。主要从事数值代数、科学计算、机器学习和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 ReviewSIAM J. Scientific ComputingSIAM J. Matrix Analysis and ApplicationSIAM J Numerical AnalysisIEEE TPAMIPatten Recognition, 以及NIPSCVPR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SIAM Review上发表研究论文的国内大陆学者,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45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,有两个属于其及其合作者。张振跃教授现任《计算数学》和《高校计算数学》编委。