学术报告报告题目: Linear Convergence of a Proximal Alternating Minimization Method with Extrapolation for L1-Norm Principal Component Analysis
报 告人: 汪鹏 博士
报告时间: 2021年11月22日（星期一下午）14:00-15:00
报告地点：4号楼318室
邀 请人:潘少华教授
欢迎广大师生前往
数学学院
2021年11月19日
报告摘要：A popular robust alternative of the classic principal component analysis (PCA) is the L1-norm PCA (L1-PCA), which aims to find a subspace that captures the most variation in a dataset as measured by the L1-norm. L1-PCA has shown great promise in alleviating the effect of outliers in data analytic applications. However, it gives rise to a challenging non-smooth non-convex optimization problem, for which existing algorithms are either not scalable or lack strong theoretical guarantees on their convergence behavior. In this work, we propose a proximal alternating minimization method with extrapolation (PAMe) for solving a two-block reformulation of the L1-PCA problem. We then show that for both the L1-PCA problem and its two-block reformulation, the Kurdyka-Lojasiewicz exponent at any of the limiting critical points is 1/2. This allows us to establish the linear convergence of the sequence of iterates generated by PAMe and to determine the criticality of the limit of the sequence with respect to both the L1-PCA problem and its two-block reformulation. To complement our theoretical development, we show via numerical experiments on both synthetic and real-world datasets that PAMe is competitive with a host of existing methods.