This work proposes a novel tensor train random projection (TTRP) method for dimension reduction, where the pairwise distances can be approximately preserved. Based on the tensor train format, this new random projection method can speed up the computation for high dimensional problems and requires less storage with little loss in accuracy, compared with existing methods (e.g., very sparse random projection). Our TTRP is systematically constructed through a rank-one TT-format with Rademacher random variables, which results in efficient projection with small variances. The isometry property of TTRP is proven in this work, and detailed numerical experiments with data sets (synthetic, MNIST and CIFAR-10) are conducted to demonstrate the efficiency of TTRP.

翻译：这项工作提出了一种新型的高压列车随机投影法(TTRP)用于降低维度,这样可以大致保持对称距离。根据高压列车格式,这种新的随机投影法可以加快对高维问题的计算,比现有方法(例如,非常稀少的随机投影)更精确地要求较少的储存,比现有方法(例如,非常分散的随机投影)少一些损失。我们的TTRP是用一级TT格式与Rademacher随机变量一起系统构建的,从而导致高效投影,但差异较小。TRP的等量特性在这项工作中得到证明,并用数据集(合成、MNIST和CIFAR-10)进行详细的数字实验,以展示TRP的效率。