Fast and provable tensor robust principal component analysis via scaled gradient descent

Abstract An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships interactions than matrices. When tapping into this critical advantage, a key challenge is to develop computationally efficient provably correct algorithms for extracting useful information from tensor that are simultaneously robust corruptions ill-conditioning. This paper tackles principal component analysis (RPCA), aims recover low-rank its observations contaminated by sparse corruptions, under Tucker decomposition. To minimize memory footprints, we propose directly low-dimensional factors—starting tailored spectral initialization—via scaled gradient descent (ScaledGD), coupled an iteration-varying thresholding operation adaptively remove impact corruptions. Theoretically, establish proposed algorithm converges linearly true at constant rate independent condition number, as long level not too large. Empirically, demonstrate achieves more scalable performance state-of-the-art RPCA through synthetic experiments real-world applications.