Angle Principal Component Analysis

Recently, many ℓ1-norm based PCA methods have been developed for dimensionality reduction, but they do not explicitly consider the reconstruction error. Moreover, they do not take into account the relationship between reconstruction error and variance of projected data. This reduces the robustness of algorithms. To handle this problem, a novel formulation for PCA, namely angle PCA, is proposed. Angle PCA employs ℓ2-norm to measure reconstruction error and variance of projected da-ta and maximizes the summation of ratio between variance and reconstruction error of each data. Angle PCA not only is robust to outliers but also retains PCA’s desirable property such as rotational invariance. To solve Angle PCA, we propose an iterative algorithm, which has closed-form solution in each iteration. Extensive experiments on several face image databases illustrate that our method is overall superior to the other robust PCA algorithms, such as PCA, PCA-L1 greedy, PCA-L1 nongreedy and HQ-PCA.

Authors

• Qianqian Wang Xidian University
• Quanxue Gao Xidian University
• Xinbo Gao School of Electronic Engineering, Xidian University, Xi’an, China Chongqing University of Posts and Telecommunications, Chongqing, China
• Feiping Nie Northwest Polytechnical University Xi'an

Keywords

• Machine Learning: Machine Learning
• Machine Learning: Unsupervised Learning