Tensor Factorization via Matrix Factorization

Tensor factorization arises in many machinelearning applications, such knowledge basemodeling and parameter estimation in latentvariable models. However, numerical meth-ods for tensor factorization have not reachedthe level of maturity of matrix factorizationmethods. In this paper, we propose a newmethod for CP tensor factorization that usesrandom projections to reduce the problemto simultaneous matrix diagonalization. Ourmethod is conceptually simple and also ap-plies to non-orthogonal and asymmetric ten-sors of arbitrary order. We prove that a smallnumber random projections essentially pre-serves the spectral information in the ten-sor, allowing us to remove the dependenceon the eigengap that plagued earlier tensor-to-matrix reductions. Experimentally, ourmethod outperforms existing tensor factor-ization methods on both simulated data andtwo real datasets.