Exploring Numerical Priors for Low-Rank Tensor Completion with Generalized CP Decomposition

Tensor completion is important to many areas such as computer vision, data analysis, and signal processing. Enforcing low-rank structures on completed tensors, a category of methods known as low-rank tensor completion has recently been studied extensively. While such methods attained great success, none considered exploiting numerical priors of tensor elements. Ignoring numerical priors causes loss of important information regarding the data, and therefore prevents the algorithms from reaching optimal accuracy. This work attempts to construct a new methodological framework called GCDTC (Generalized CP Decomposition Tensor Completion) for leveraging numerical priors and achieving higher accuracy in tensor completion. In this newly introduced framework, a generalized form of CP Decomposition is applied to low-rank tensor completion. This paper also proposes an algorithm known as SPTC (Smooth Poisson Tensor Completion) for nonnegative integer tensor completion as an instantiation of the GCDTC framework. A series of experiments on real-world data indicated that SPTC could produce results superior in completion accuracy to current state-of-the-arts.Comment: 11 pages, 4 figures, 3 pseudocode algorithms, and 1 tabl

Tensor Completion via Leverage Sampling and Tensor QR Decomposition for Network Latency Estimation

In this paper, we consider the network latency estimation, which has been an important metric for network performance. However, a large scale of network latency estimation requires a lot of computing time. Therefore, we propose a new method that is much faster and maintains high accuracy. The data structure of network nodes can form a matrix, and the tensor model can be formed by introducing the time dimension. Thus, the entire problem can be be summarized as a tensor completion problem. The main idea of our method is improving the tensor leverage sampling strategy and introduce tensor QR decomposition into tensor completion. To achieve faster tensor leverage sampling, we replace tensor singular decomposition (t-SVD) with tensor CSVD-QR to appoximate t-SVD. To achieve faster completion for incomplete tensor, we use the tensor $L_{2,1}$-norm rather than traditional tensor nuclear norm. Furthermore, we introduce tensor QR decomposition into alternating direction method of multipliers (ADMM) framework. Numerical experiments witness that our method is faster than state-of-art algorithms with satisfactory accuracy.Comment: 20 pages, 7 figure