An Analysis of Tensor Models for Learning on Structured Data

While tensor factorizations have become increasingly popular for learning on various forms of structured data, only very few theoretical results exist on the generalization abilities of these methods. Here, we discuss the tensor product as a principled way to represent structured data in vector spaces for machine learning tasks. To derive generalization error bounds for tensor factorizations, we extend known bounds for matrix factorizations to the tensor case. Furthermore, we analyze experimentally and analytically how tensor factorization behaves for learning on overand understructured representations, for instance, when matrix factorizations are applied to tensor data.