title: Avoiding Optimal Mean ℓ2,1-Norm Maximization-Based Robust PCA for Reconstruction.
abstract: Robust principal component analysis (PCA) is one of the most important dimension-reduction techniques for handling high-dimensional data with outliers. However, most of the existing robust PCA presupposes that the mean of the data is zero and incorrectly utilizes the average of data as the optimal mean of robust PCA. In fact, this assumption holds only for the squared [Formula: see text]-norm-based traditional PCA. In this letter, we equivalently reformulate the objective of conventional PCA and learn the optimal projection directions by maximizing the sum of projected difference between each pair of instances based on [Formula: see text]-norm. The proposed method is robust to outliers and also invariant to rotation. More important, the reformulated objective not only automatically avoids the calculation of optimal mean and makes the assumption of centered data unnecessary, but also theoretically connects to the minimization of reconstruction error. To solve the proposed nonsmooth problem, we exploit an efficient optimization algorithm to soften the contributions from outliers by reweighting each data point iteratively. We theoretically analyze the convergence and computational complexity of the proposed algorithm. Extensive experimental results on several benchmark data sets illustrate the effectiveness and superiority of the proposed method.
authors.affiliation: SPKLSTN Lab, Department of Computer Science, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China minnluo@xjtu.edu.cn.
authors.forename: Minnan
authors.initials: M
authors.lastname: Luo
authors.affiliation: Center for OPTical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China feipingnie@gmail.com.
authors.forename: Feiping
authors.initials: F
authors.lastname: Nie
authors.affiliation: Centre for Quantum Computation and Intelligent Systems, University of Technology Sydney, Sydney, 2007 NSW, Australia cxj273@gmail.com.
authors.forename: Xiaojun
authors.initials: X
authors.lastname: Chang
authors.affiliation: Centre for Quantum Computation and Intelligent Systems, University of Technology Sydney, Sydney, 2007 NSW, Australia yee.i.yang@gmail.com.
authors.forename: Yi
authors.initials: Y
authors.lastname: Yang
authors.affiliation: School of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A. alex@cs.cmv.edu.
authors.forename: Alexander G
authors.initials: AG
authors.lastname: Hauptmann
authors.affiliation: SPKLSTN Lab, Department of Computer Science, Xi'an Jiatong University, Xi'an, Shaanxi 710049, China qhzheng@mail.xjtu.edu.cn.
authors.forename: Qinghua
authors.initials: Q
authors.lastname: Zheng