Data Subdivision Based Dual-Weighted Robust Principal Component Analysis

Abstract

Principal Component Analysis (PCA) is one of the most important unsupervised dimensionality reduction algorithms, which uses squared $\ell _{2}$ -norm to make it very sensitive to outliers. Those improved versions based on $\ell _{1}$ -norm alleviate this problem, but they have other shortcomings, such as optimization difficulties or lack of rotational invariance, etc. Besides, existing methods only vaguely divide normal samples and outliers to improve robustness, but they ignore the fact that normal samples can be more specifically divided into positive samples and hard samples, which should have different contributions to the model because positive samples are more conducive to learning the projection matrix. In this paper, we propose a novel Data Subdivision Based Dual-Weighted Robust Principal Component Analysis, namely DRPCA, which firstly designs a mark vector to distinguish normal samples and outliers, and directly removes outliers according to mark weights. Moreover, we further divide normal samples into positive samples and hard samples by self-constrained weights, and place them in relative positions, so that the weight of positive samples is larger than hard samples, which makes the projection matrix more accurate. Additionally, the optimal mean is employed to obtain a more accurate data center. To solve this problem, we carefully design an effective iterative algorithm and analyze its convergence. Experiments on real-world and RGB large-scale datasets demonstrate the superiority of our method in dimensionality reduction and anomaly detection.