The problem of tensor completion is important to many areas such as computer vision, data analysis, signal processing, etc. Previously, a category of methods known as low-rank tensor completion has been proposed and developed, involving the enforcement of low-rank structures on completed tensors. While such methods have been constantly improved, none have previously considered exploiting the numerical properties of tensor elements. This work attempts to construct a new methodological framework called GCDTC (Generalized CP Decomposition Tensor Completion) based on these properties. In this newly introduced framework, the CP Decomposition is reformulated as a Maximum Likelihood Estimate (MLE) problem, and generalized via the introduction of differing loss functions. The generalized decomposition is subsequently applied to low-rank tensor completion. Such loss functions can also be easily adjusted to consider additional factors in completion, such as smoothness, standardization, etc. An example of nonnegative integer tensor decomposition via the Poisson CP Decomposition is given to demonstrate the new methodology's potentials. Through experimentation with real-life data, it is confirmed that this method could produce results superior to current state-of-the-art methodologies. It is expected that the proposed notion would inspire a new set of tensor completion methods based on the generalization of decompositions, thus contributing to related fields.

翻译：高压完成问题对于计算机视觉、数据分析、信号处理等许多领域都很重要。以前,已经提出和开发了被称为低压完成率的一类方法,其中包括对完成的低压完成率执行低压完成率结构。虽然这些方法不断改进,但以前没有考虑利用高压元素的数值属性。根据这些属性,努力建立一个称为GCDTC(普遍CP分解天线完成)的新的方法框架。在这个新引入的框架中,CP分解被重新确定为最大相似度估计(MLE)问题,并通过引入不同的损失功能加以普及。普遍分解随后适用于低压完成率的Exor完成率结构。这种损失功能也可以很容易地进行调整,以考虑更多的完成因素,例如平滑、标准化等。通过Poisson CP Decomposition(Poisson CP Decomposi)来证明新方法的潜力。通过对现实生活数据进行实验,它证实这一方法可以产生优于目前基于标准完成率的预期方法。