TT-LSQR for tensor least squares problems and application to data mining

We are interested in the numerical solution of the tensor least squares problem (Formula presented.) where X∈Rm1×m2×⋯×md, F∈Rn1×n2×⋯×nd are tensors with d dimensions, and the coefficients Aj(i) are tall matrices of conforming dimensions. We first describe a tensor implementation of the classical LSQR method by Paige and Saunders, using the tensor-train representation as key ingredient. We also show how to incorporate sketching to lower the computational cost of dealing with the tall matrices Aj(i). We then use this methodology to address a problem in information retrieval, the classification of a new query document among already categorized documents, according to given keywords.