Rademacher Random Projections with Tensor Networks

Random projection (RP) have recently emerged as popular techniques in themachine learning community for their ability in reducing the dimension of veryhigh-dimensional tensors. Following the work in [29], we consider a tensorizedrandom projection relying on Tensor Train (TT) decomposition where each elementof the core tensors is drawn from a Rademacher distribution. Our theoreticalresults reveal that the Gaussian low-rank tensor represented in compressed formin TT format in [29] can be replaced by a TT tensor with core elements drawnfrom a Rademacher distribution with the same embedding size. Experiments onsynthetic data demonstrate that tensorized Rademacher RP can outperform thetensorized Gaussian RP studied in [29]. In addition, we show both theoreticallyand experimentally, that the tensorized RP in the Matrix Product Operator (MPO)format proposed in [5] for performing SVD on large matrices is not a Johnson-Lindenstrauss transform (JLT) and therefore not a well-suited random projectionmap