由 Slim Transforms 赋能的精确张量补全
Exact Tensor Completion Powered by Slim Transforms
AI总结：
针对现有张量补全理论要求变换正交的限制，本文建立任意线性变换下精确张量补全的理论保证，揭示slim transforms更优的理论原因，提升方法灵活性并经实验验证其优越性。
摘要：
本文研究了张量补全问题，该问题旨在从部分观测值中完美恢复张量。现有理论保证要求所涉及的变换是正交的，这阻碍了其应用。本文跳出各向同性和自伴性的约束，通过直接在变换域中对张量进行操作，建立了任意线性变换下精确张量补全的理论保证。随着变换选择的丰富，通过证明得到的新分析从理论层面揭示了为什么 slim transforms 优于其方形对应变换。我们的模型和证明极大地提升了张量补全的灵活性，大量实验验证了所提方法的优越性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
