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. Whilst 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 indicate that SPTC could produce results superior in completion accuracy to current state-of-the-art methods. Related code is available in the supplemental materials.