Tensor Factorization via Matrix Factorization

TL;DR

This paper introduces a novel tensor factorization method using random projections to reduce the problem to matrix diagonalization, improving efficiency and applicability to various tensor types.

Contribution

The paper presents a simple, effective tensor factorization approach that preserves spectral information without relying on eigengaps, applicable to non-orthogonal and asymmetric tensors.

Findings

Outperforms existing methods on simulated data

Effective for non-orthogonal and asymmetric tensors

Reduces dependence on eigengap assumptions

Abstract

Tensor factorization arises in many machine learning applications, such knowledge base modeling and parameter estimation in latent variable models. However, numerical methods for tensor factorization have not reached the level of maturity of matrix factorization methods. In this paper, we propose a new method for CP tensor factorization that uses random projections to reduce the problem to simultaneous matrix diagonalization. Our method is conceptually simple and also applies to non-orthogonal and asymmetric tensors of arbitrary order. We prove that a small number random projections essentially preserves the spectral information in the tensor, allowing us to remove the dependence on the eigengap that plagued earlier tensor-to-matrix reductions. Experimentally, our method outperforms existing tensor factorization methods on both simulated data and two real datasets.