A generalizable framework for low-rank tensor completion with numerical priors

• Published in: Pattern recognition 2024-11, Vol.155, p.110678, Article 110678
• Main Authors: Yuan, Shiran, Huang, Kaizhu
• Format: Article
• Language: English
• Subjects: Block coordinate descent; CP decomposition; Missing data; Prior distributions; Tensorial representations
• ISSN: 0031-3203; 1873-5142
• DOI: 10.1016/j.patcog.2024.110678

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. •Numerical priors are useful for tensor completion but were often overlooked.•We exploit them generalizably using a probabilistic model and an algorithm.•Our framework is also compatible with priors describing the tensor’s structure.•Using the framework, we devise a new method for non-negative tensor completion.•We conducted experiments and show that our method achieves SOTA accuracy.