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

    來自: 數學與統計學院       作者:   編輯:邱楠       時間:2019-04-30





    報告摘要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.



    張振躍,男,浙江大學數學學院二級教授,博士生導師,浙江大學信息數學研究所所長。2013年獲浙江大學心平教學杰出貢獻獎,2014年獲國務院政府津貼。主要從事數值代數、科學計算、機器學習和大數據分析等研究領域的模型與算法的理論分析與計算。先后在在國際著名學術刊物SIAM Review、SIAM J. Scientific Computing、SIAM J. Matrix Analysis and Application、SIAM J Numerical Analysis、IEEE TPAMI、Patten Recognition, 以及NIPS、CVPR等會議上發表80余篇研究論文,在相關研究中取得了受到許多國際關注的系統性研究成果。他是第一位在SIAM Review上發表研究論文的國內大陸學者,其關于非線性降維算法的工作,多年來一直列SIAM J. Scientific Computing 10年高引用率第4、5位。在國際機器學習領域中被廣泛應用的Scikit-Learn中收錄的8個關于流形學習的經典算法中,有兩個屬于其及其合作者。張振躍教授現任《計算數學》和《高校計算數學》編委。