Monday, February 09, 2015

Tensor Factorization via Matrix Factorization

Using random projections for tensors is not the first time we see this but here let us note why:
...We overcome both these limitations using O(log(k)) random projections of the tensor. Note that our use of random projections is atypical: instead of using projections for dimensionality reduction (e.g. [32]), we use it to reduce the order of the tensor.
Without further ado here is: Tensor Factorization via Matrix Factorization by Volodymyr Kuleshov, Arun Tejasvi Chaganty, Percy Liang

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.
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