论文标题
张量火车随机投影
Tensor Train Random Projection
论文作者
论文摘要
这项工作提出了一种新型的张量列车随机投影（TTRP）方法，用于降低尺寸，其中成对距离近似保留。我们的TTRP是通过张量列（TT）表示的，其TT量量等于1。基于张量列车格式，与现有方法相比，这种新的随机投影方法可以加快高维数据集的尺寸缩小程序，并且需要较小的存储成本，而准确性却很少损失。我们提供了TTRP的偏差和方差的理论分析，这表明该方法是具有有界方差的预期等距投影，我们表明Rademacher分布是生成相应TT核的最佳选择。使用合成数据集和MNIST数据集进行了详细的数值实验，以证明TTRP的效率。
This work proposes a novel tensor train random projection (TTRP) method for dimension reduction, where pairwise distances can be approximately preserved. Our TTRP is systematically constructed through a tensor train (TT) representation with TT-ranks equal to one. Based on the tensor train format, this new random projection method can speed up the dimension reduction procedure for high-dimensional datasets and requires less storage costs with little loss in accuracy, compared with existing methods. We provide a theoretical analysis of the bias and the variance of TTRP, which shows that this approach is an expected isometric projection with bounded variance, and we show that the Rademacher distribution is an optimal choice for generating the corresponding TT-cores. Detailed numerical experiments with synthetic datasets and the MNIST dataset are conducted to demonstrate the efficiency of TTRP.
