Max–Min Robust Principal Component Analysis

Principal Component Analysis (PCA) is a powerful unsupervised dimensionality reduction algorithm, which uses squared ℓ₂-norm to cleverly connect reconstruction error and projection variance, and those improved PCA methods only consider one of them, which limits their performance. To alleviate this problem, we propose a novel Max–Min Robust Principal Component Analysis via binary weight, which ingeniously combines reconstruction error and projection variance to learn projection matrix more accurately, and uses ℓ₂-norm as evaluation criterion to make the model rotation invariant. In addition, we design binary weight to remove outliers to improve the robustness of model and obtain the ability of anomaly detection. Subsequently, we exploit an efficient iterative optimization algorithm to solve this problem. Extensive experimental results show that our model outperforms related state-of-the-art PCA methods.