Tensorized Random Projections

by   Beheshteh T. Rakhshan, et al.

We introduce a novel random projection technique for efficiently reducing the dimension of very high-dimensional tensors. Building upon classical results on Gaussian random projections and Johnson-Lindenstrauss transforms (JLT), we propose two tensorized random projection maps relying on the tensor train (TT) and CP decomposition format, respectively. The two maps offer very low memory requirements and can be applied efficiently when the inputs are low rank tensors given in the CP or TT format. Our theoretical analysis shows that the dense Gaussian matrix in JLT can be replaced by a low-rank tensor implicitly represented in compressed form with random factors, while still approximately preserving the Euclidean distance of the projected inputs. In addition, our results reveal that the TT format is substantially superior to CP in terms of the size of the random projection needed to achieve the same distortion ratio. Experiments on synthetic data validate our theoretical analysis and demonstrate the superiority of the TT decomposition.



There are no comments yet.


page 1

page 2

page 3

page 4


Rademacher Random Projections with Tensor Networks

Random projection (RP) have recently emerged as popular techniques in th...

Tensor Random Projection for Low Memory Dimension Reduction

Random projections reduce the dimension of a set of vectors while preser...

Multilinear Low-Rank Tensors on Graphs & Applications

We propose a new framework for the analysis of low-rank tensors which li...

Tensor Train Random Projection

This work proposes a novel tensor train random projection (TTRP) method ...

Parallel Nonnegative CP Decomposition of Dense Tensors

The CP tensor decomposition is a low-rank approximation of a tensor. We ...

Randomized Sketches of Convex Programs with Sharp Guarantees

Random projection (RP) is a classical technique for reducing storage and...

TEC: Tensor Ensemble Classifier for Big Data

Tensor (multidimensional array) classification problem has become very p...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.