Tensor completion is important to many areas such as computer vision, data analysis, and signal processing. 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 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 numerical properties to achieve higher accuracy in tensor completion. In this newly introduced framework, a generalized form of the 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 application of the GCDTC framework. Through experimentation with real-life data, it is verified that this method could produce results superior in completion accuracy to current state-of-the-art methodologies.
翻译:电锯的完成对于计算机视觉、数据分析和信号处理等许多领域都很重要。以前,已经提出并开发了一类称为低级高压完成率的方法,其中包括对完成的高压实施低级结构。虽然这些方法不断改进,但没有考虑利用高压元素的数值属性。这项工作试图在数字属性的基础上建立一个称为GCDTC(通用CP分解 Tensor 完成率)的新的方法框架,以便实现更精确的推敲完成率。在这个新引入的框架中,对低级高压完成率应用了一种通用的氯化石蜡分解法形式。本文还提出一种称为COPMC(Smooth Poisson Tensor完成率)的算法,作为GCDTC框架的一种应用。通过对实际寿命数据进行实验,可以核实这种方法在完成率上会优于目前的最新方法。</s>