We introduce a framework for the modelling of multivariate functions that are well approximated by a sum of (few) separable terms. The framework proposes to approximate each component function by a B-spline, resulting in an approximant where the underlying coefficient tensor of the tensor product expansion has a low rank polyadic decomposition parametrization. By exploiting the multilinear structure, as well as the sparsity pattern of the compactly supported B-spline basis terms, we demonstrate how such an approximant is well-suited for approximation, regression and classification tasks by using the Gauss–Newton algorithm as a workhorse to train the parameters. Numerical examples will illustrate the effectiveness of the approach.
This is joint work with Nithin Govindarajan (KU Leuven) and Nico Vervliet (KU Leuven).