Robust Transfer Principal Component Analysis with Rank Constraints

Principal component analysis (PCA), a well-established technique for data analysis and processing, provides a convenient form of dimensionality reduction that is effective for cleaning small Gaussian noises presented in the data. However, the applicability of standard principal component analysis in real scenarios is limited by its sensitivity to large errors. In this paper, we tackle the challenge problem of recovering data corrupted with errors of high magnitude by developing a novel robust transfer principal component analysis method. Our method is based on the assumption that useful information for the recovery of a corrupted data matrix can be gained from an uncorrupted related data matrix. Specifically, we formulate the data recovery problem as a joint robust principal component analysis problem on the two data matrices, with shared common principal components across matrices and individual principal components specific to each data matrix. The formulated optimization problem is a minimization problem over a convex objective function but with non-convex rank constraints. We develop an efficient proximal projected gradient descent algorithm to solve the proposed optimization problem with convergence guarantees. Our empirical results over image denoising tasks show the proposed method can effectively recover images with random large errors, and significantly outperform both standard PCA and robust PCA.