Tensor Factorization via Matrix Factorization
This work addresses a bottleneck in tensor factorization for applications like knowledge base modeling, offering a novel solution with practical improvements.
The paper tackles the problem of tensor factorization, which is less mature than matrix factorization, by proposing a method using random projections to reduce CP tensor factorization to simultaneous matrix diagonalization. The method outperforms existing approaches on simulated and real datasets.
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.