A generalizable framework for low-rank tensor completion with numerical priors
This work addresses the limitation of ignoring numerical priors in tensor completion, which is crucial for improving accuracy in data analysis applications, though it is incremental as it builds on existing low-rank methods.
The authors tackled the problem of low-rank tensor completion by introducing a generalizable framework that incorporates numerical priors, resulting in the SPTC algorithm which outperforms state-of-the-art methods by considerable margins in non-negative tensor completion tasks.
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.