报告题目: Convergence Analysis of the Oja-Karhunen Algorithm for Principal Component Analysis
报告人： 梁鑫 博士
报告人单位：清华大学
报告时间：2018年12月8日,下午14：00-15:30
报告地点：数学学院第一报告厅
报告摘要:
Processing streaming data as they arrive is often necessary for high dimensional data analysis. In this talk, we analyze the convergence of a subspace online PCA iteration. Under the sub-Gaussian assumption, we obtain the finite-sample error bound that closely matches the minimax information lower bound by Vu and Lei [Ann. Statist. 41:6(2013), 2905-2947]. The case for the most significant principal component only, was solved by Li, Wang, Liu, and Zhang [Math. Program., Ser. B, DOI 10.1007/s10107-017-1182-z], but a straightforward extension of their proofs, however, does not seem to work for the subspace case. People may see matrix analysis plays an important role in generalizing results for one-dimensional case to those for multi-dimensional case.
报告人介绍：
梁鑫，2014年于北京大学数学科学学院获得理学博士学位。其后分别在马克斯普朗克复杂技术系统动力学研究所、新竹交通大学从事博士后研究。2018年起于清华大学丘成桐数学科学中心任助理教授，从事矩阵理论和数值线性代数方向的研究，重点关注特征值问题的理论分析及其在偏微分方程、数据科学中的应用。