Tensor Random Projection for Low Memory Dimension Reduction

Abstract

Random projections reduce the dimension of a set of vectors while preserving structural information, such as distances between vectors in the set. This paper proposes a novel use of row-product random matrices in random projection, where we call it Tensor Random Projection (TRP). It requires substantially less memory than existing dimension reduction maps. The TRP map is formed as the Khatri-Rao product of several smaller random projections, and is compatible with any base random projection including sparse maps, which enable dimension reduction with very low query cost and no floating point operations. We also develop a reduced variance extension. We provide a theoretical analysis of the bias and variance of the TRP, and a non-asymptotic error analysis for a TRP composed of two smaller maps. Experiments on both synthetic and MNIST data show that our method performs as well as conventional methods with substantially less storage.

arXiv commentIn NeurIPS Workshop on Relational Representation Learning (2018)

References in corpus (2)

• Fast and Guaranteed Tensor Decomposition via Sketching
• Johnson-Lindenstrauss Compression with Neuroscience-Based Constraints

Cited by in corpus (7)

• Guarantees for the Kronecker Fast Johnson-Lindenstrauss Transform Using a Coherence and Sampling Argument
• Fast and Accurate Randomized Algorithms for Low-rank Tensor Decompositions
• FrequentNet: A Novel Interpretable Deep Learning Model for Image Classification
• Tensorized Random Projections
• Parallel algorithms for computing the tensor-train decomposition
• Rademacher Random Projections with Tensor Networks
• Tensorization of neural networks for improved privacy and interpretability