论文标题
张量环分解的基于抽样的方法
A Sampling-Based Method for Tensor Ring Decomposition
论文作者
论文摘要
我们提出了一种基于抽样的方法，用于计算数据张量的张量环（TR）分解。该方法使用杠杆评分采样的交替正方形，以迭代方式安装TR芯。通过利用TR量的特殊结构，我们可以有效地估计杠杆评分，并达到一种在输入张量量的次数中具有复杂性倍率的方法。我们为采样最小二乘问题提供了高概率的相对错误保证。我们将我们的建议与合成和真实数据实验中的现有方法进行了比较。我们的方法在竞争方法上实现了实力的速度 - 有时是两个或三个数量级 - 同时保持良好的准确性。我们还提供了一个示例，说明如何将我们的方法用于快速提取。
We propose a sampling-based method for computing the tensor ring (TR) decomposition of a data tensor. The method uses leverage score sampled alternating least squares to fit the TR cores in an iterative fashion. By taking advantage of the special structure of TR tensors, we can efficiently estimate the leverage scores and attain a method which has complexity sublinear in the number of input tensor entries. We provide high-probability relative-error guarantees for the sampled least squares problems. We compare our proposal to existing methods in experiments on both synthetic and real data. Our method achieves substantial speedup -- sometimes two or three orders of magnitude -- over competing methods, while maintaining good accuracy. We also provide an example of how our method can be used for rapid feature extraction.
