论文标题
Grassmannian优化在线张量完成和通过T-SVD进行跟踪
Grassmannian Optimization for Online Tensor Completion and Tracking with the t-SVD
论文作者
论文摘要
我们为使用张量的单数值分解（T-SVD）代数框架提出了一种新的快速流算法，以解决张量的完成问题。我们显示T-SVD是三阶张量的良好的块 - 期分解的专业化，并且我们在此模型下提出了一种算法，可以跟踪从不完整的流式流式2-D数据中更改自由的subsodules。所提出的算法使用子空间的Grassmann歧管上的增量梯度下降的原理来解决张量的完成问题，并在时间样本数量中使用线性复杂性和恒定内存来解决。我们为算法提供了局部预期的线性收敛结果。我们的经验结果在准确性方面具有竞争力，但计算时间比最新的张量完成算法要快得多，在有限的采样下，在实际应用上恢复了时间化学化学感应和MRI数据。
We propose a new fast streaming algorithm for the tensor completion problem of imputing missing entries of a low-tubal-rank tensor using the tensor singular value decomposition (t-SVD) algebraic framework. We show the t-SVD is a specialization of the well-studied block-term decomposition for third-order tensors, and we present an algorithm under this model that can track changing free submodules from incomplete streaming 2-D data. The proposed algorithm uses principles from incremental gradient descent on the Grassmann manifold of subspaces to solve the tensor completion problem with linear complexity and constant memory in the number of time samples. We provide a local expected linear convergence result for our algorithm. Our empirical results are competitive in accuracy but much faster in compute time than state-of-the-art tensor completion algorithms on real applications to recover temporal chemo-sensing and MRI data under limited sampling.
