Low-Rank Tensor Completion, a method which exploits the inherent structure of tensors, has been studied extensively as an effective approach to tensor completion. Whilst such methods attained great success, none have systematically considered exploiting the 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. Despite the existence of some individual works which consider ad hoc numerical priors for specific tasks, no generalizable frameworks for incorporating numerical priors have appeared. We present the Generalized CP Decomposition Tensor Completion (GCDTC) framework, the first generalizable framework for low-rank tensor completion that takes numerical priors of the data into account. We test GCDTC by further proposing the Smooth Poisson Tensor Completion (SPTC) algorithm, an instantiation of the GCDTC framework, whose performance exceeds current state-of-the-arts by considerable margins in the task of non-negative tensor completion, exemplifying GCDTC's effectiveness. Our code is open-source.

翻译：低秩张量补全作为一种利用张量内在结构的有效方法，已在张量补全领域得到广泛研究。尽管此类方法取得了巨大成功，但尚未有系统性地考虑利用张量元素的数值先验。忽略数值先验会导致丢失数据的重要信息，从而阻碍算法达到最优精度。尽管存在一些针对特定任务考虑特定数值先验的独立工作，但尚未出现可泛化的数值先验融合框架。本文提出广义CP分解张量补全框架，这是首个考虑数据数值先验的可泛化低秩张量补全框架。我们通过进一步提出平滑泊松张量补全算法来验证GCDTC框架，该算法作为GCDTC框架的具体实例，在非负张量补全任务中以显著优势超越当前最优方法，从而验证了GCDTC框架的有效性。我们的代码已开源。