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[数学论坛]Least-Square Approach to Out-of-Sample Extension of Dimensionality Reduction for Diffusion Maps
发布日期:2018-06-29  浏览量:

报告题目Least-Square Approach to Out-of-Sample Extension of Dimensionality Reduction for Diffusion Maps    

报告人ProfessorJianzhong Wang

报告人单位:美国得克萨斯州山姆休斯顿大学

报告时间:2018.06.14   14:30-15:30      

报告地点:老主楼321学术交流厅

摘要:Let be a data set in , where is the trainning set and   the testing one. Assume that a kernel method produces a dimensionality reduction (DR) mapping that maps the high-dimensional data   to its row-dimensional representation . The out-of-sample extension of dimensionality reduction problem is to find the dimensionality reduction of using the extension of   instead of re-training the whole set In this talk, utilizing the framework of reproducing kernel Hilbert space (RKHS)  theory, we introduce a least square approach to extensions of DR mapping, establish a new mathematical theory, which provides a uniform treatment of many popular out-of-sample algorithms, and give the error analysis of the extension. Particularly, we provide a detailed discussion on the extensions of the diffusion maps. We also illustrate the validity of the new developed algorithms in several examples.

报告人简介:王建忠教授现任美国得克萨斯州山姆休斯顿大学教授。本毕业于北京大学数学力学系,1981年获浙江大学应用数学系硕士学位。历任武汉大学教授,香港中文大学客座教授等。主要研究方向包括:样条和逼近理论、小波分析、图像处理以及高维数据分析等。曾主持多项美国自然科学基金及其他基金课题研究。发表学术论文90余篇,专利1项。

邀请人:陈迪荣

     

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