Energy-Based Non-Negative Tensor Factorization via Multi-Body Modeling

Tensor factorization has fundamental difficulties in rank tuning and optimization. To avoid these difficulties, we develop a rank-free energy-based tensor factorization, called many-body approximation, that allows intuitive modeling of tensors and global optimization. Our approach models tensors as distributions via the energy function, which describes interactions between modes, and a dually flat statistical manifold is induced. We visualize these interactions as tensor networks and reveal a nontrivial relationship between many-body approximation and low-rank approximation.