Abstract
Tensor Robust Principal Component Analysis (TRPCA) plays a critical role in handling high multi-dimensional data sets, aiming to recover the low-rank and sparse components both accurately and efficiently. In this paper, different from current approach, we developed a new t-Gamma tensor quasi-norm as a non-convex regularization to approximate the low-rank component. Compared to various convex regularization, this new configuration not only can better capture the tensor rank but also provides a simplified approach. An optimization process is conducted via tensor singular decomposition and an efficient augmented Lagrange multiplier algorithm is established. Extensive experimental results demonstrate that our new approach outperforms current state-of-the-art algorithms in terms of accuracy and efficiency.
Highlights
An array of numbers arranged on a regular grid with a variable number of axes is described as a tensor
Robust Principal Component Analysis (RPCA) [4,5,6,7,8], aiming to recover the low-rank and sparse matrices both accurately and efficiently, has been widely studied in data compressed sensing and computer vision. It is of great use when we try to solve the problem of subspace learning or Principal Component Analysis (PCA) in the presence of outliers [9]
We explore the Tensor Robust Principal Component Analysis (TRPCA) method based on the non-convex t-Gamma quasi-norm of 3rd-order tensors
Summary
An array of numbers arranged on a regular grid with a variable number of axes is described as a tensor. Robust Principal Component Analysis (RPCA) [4,5,6,7,8], aiming to recover the low-rank and sparse matrices both accurately and efficiently, has been widely studied in data compressed sensing and computer vision. It is of great use when we try to solve the problem of subspace learning or Principal Component Analysis (PCA) in the presence of outliers [9]. Tensor Robust Principal Component Analysis (TRPCA) extends the RPCA from matrix to the tensor case, that is, to recover a low-rank tensor and a sparse (noise entries) tensor
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have