Truncated Robust Principle Component Analysis With A General Optimization Framework

Recently, several robust principle component analysis (RPCA) models have been proposed to improve the robustness of principle component analysis (PCA) model. However, an obvious problem that the improvement of robustness on outliers affects the discrimination of correct samples, has not been solved yet. In this paper, we aim to treat correct samples and outliers differently via proposing a truncated robust principle component analysis model (T-RPCA). The proposed T-RPCA model has high interpretation for the robustness of outliers and discrimination of correct samples. Moreover, we propose a general optimization framework named re-weighted (RW) framework to solve a general optimization problem and generalize two sub-frameworks upon it. 1) The first one orients a general truncation loss optimization problem which contains objective problem of T-RPCA model. 2) The second sub-framework focuses on a general singular-value based optimization problem which is useful in many problems. Besides, we provide rigorously theoretical guarantees for proposed model, optimization framework and sub-frameworks. Empirical studies demonstrate that the proposed T-PRCA outperform than previous RPCA methods for reconstruction and classification tasks.