论文标题
基于抽样的分解算法，用于任意张量网络
Sampling-Based Decomposition Algorithms for Arbitrary Tensor Networks
论文作者
论文摘要
我们展示了如何开发基于采样的交替平方（ALS）算法，以将张量分解为任何张量网络（TN）格式。只要TN格式满足某些温和的假设，则由此产生的算法将具有输入的sublinear每卷成本。与以前的大多数基于采样的ALS方法进行张量分解的方法不同，我们框架中的采样是根据ALS子问题中设计矩阵的确切杠杆得分分布进行的。我们实施和测试了两种张量分解算法，这些算法在功能提取实验中使用我们的采样框架，我们将它们与许多其他分解算法进行比较。
We show how to develop sampling-based alternating least squares (ALS) algorithms for decomposition of tensors into any tensor network (TN) format. Provided the TN format satisfies certain mild assumptions, resulting algorithms will have input sublinear per-iteration cost. Unlike most previous works on sampling-based ALS methods for tensor decomposition, the sampling in our framework is done according to the exact leverage score distribution of the design matrices in the ALS subproblems. We implement and test two tensor decomposition algorithms that use our sampling framework in a feature extraction experiment where we compare them against a number of other decomposition algorithms.
