Accurate Tensor Decomposition with Simultaneous Rank Approximation for Surveillance Videos

Canonical polyadic (CP) decomposition of a tensor is a basic operation in a lot of applications such as data mining and video foreground/background separation. However, existing algorithms for CP decomposition require users to provide a rank of the target tensor data as part of the input and finding the rank of a tensor is an NP-hard problem. Currently, to perform CP decomposition, users are required to make an informed guess of a proper tensor rank based on the data at hand, and the result may still be suboptimal. In this paper, we propose to conduct CP decomposition and tensor rank approximation together, so that users do not have to provide the proper rank beforehand, and the decomposition algorithm will find the proper rank and return a high-quality result. We formulate an optimization problem with an objective function consisting of a least-squares Tikhonov regularization and a sparse l1-regularization term. We also test its effectiveness over real applications with moving object videos.