Tensor Train Random Projection
This addresses the computational and storage bottlenecks in dimension reduction for high-dimensional data, representing an incremental improvement over existing random projection methods.
The paper tackles the problem of dimension reduction for high-dimensional datasets by proposing a tensor train random projection (TTRP) method that preserves pairwise distances approximately. The result shows that TTRP speeds up the procedure and reduces storage costs with little accuracy loss compared to existing methods, as demonstrated in numerical experiments with synthetic and MNIST datasets.
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.