  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.
