Exact Tensor Completion Powered by Slim Transforms
This work enhances flexibility in tensor completion for applications in data analysis and machine learning, though it is incremental as it builds on existing theoretical frameworks.
The paper tackles the tensor completion problem by establishing a theoretical guarantee for exact recovery using arbitrary linear transforms, eliminating the need for orthogonal constraints, and demonstrates that slim transforms outperform square ones in experiments.
In this work, a tensor completion problem is studied, which aims to perfectly recover the tensor from partial observations. The existing theoretical guarantee requires the involved transform to be orthogonal, which hinders its applications. In this paper, jumping out of the constraints of isotropy and self-adjointness, the theoretical guarantee of exact tensor completion with arbitrary linear transforms is established by directly operating the tensors in the transform domain. With the enriched choices of transforms, a new analysis obtained by the proof discloses why slim transforms outperform their square counterparts from a theoretical level. Our model and proof greatly enhance the flexibility of tensor completion and extensive experiments validate the superiority of the proposed method.