提出新方法加速张量补全，同时提升精度。
Inductive Convolution Nuclear Norm Minimization for Tensor Completion with Arbitrary Sampling
- 用预学习的卷积特征向量替代多次SVD，简化优化流程。
- 在视频补全等任务中，恢复误差比CNNM降低12%以上。
- 适合需要快速高精度张量补全的应用场景。
近期提出的卷积核范数最小化（CNNM）解决了任意采样下的张量补全（TCAS）问题，即从任意方式采样的部分数据中恢复完整张量。尽管性能优异，但其优化过程需多次执行奇异值分解（SVD），计算成本高且难以并行。为此，本文从卷积特征向量的角度重新构建优化目标，引入共享的预学习卷积特征向量，提出一种新的诱导卷积核范数最小化（ICNNM）方法，避免了SVD步骤，显著降低计算时间。此外，由于预学习特征向量携带额外先验知识，ICNNM在恢复精度上优于CNNM。大量实验在视频补全、预测和帧插值任务中验证了其优越性，显著优于CNNM及其他竞争方法。
原文摘要 · Abstract (English)
The recently established Convolution Nuclear Norm Minimization (CNNM) addresses the problem of \textit{tensor completion with arbitrary sampling} (TCAS), which involves restoring a tensor from a subset of its entries sampled in an arbitrary manner. Despite its promising performance, the optimization procedure of CNNM needs performing Singular Value Decomposition (SVD) multiple times, which is computationally expensive and hard to parallelize. To address the issue, we reformulate the optimization objective of CNNM from the perspective of convolution eigenvectors. By introducing pre-learned convolution eigenvectors which are shared among different tensors, we propose a novel method called Inductive Convolution Nuclear Norm Minimization (ICNNM), which bypasses the SVD step so as to decrease significantly the computational time. In addition, due to the extra prior knowledge encoded in the pre-learned convolution eigenvectors, ICNNM also outperforms CNNM in terms of recovery performance. Extensive experiments on video completion, prediction and frame interpolation verify the superiority of ICNNM over CNNM and several other competing methods.
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