Hierarchical alternating nonlinear least squares for nonnegative matrix factorization using rational functions

We present an extension of the widely used Hierarchical Alternating Least Squares (HALS) algorithm to solve Nonnegative Matrix Factorization (NMF) problems using rational functions, in order to unmix discretization of continuous signals. We observe that the use of rational functions in NMF can significantly improve the quality of the reconstruction of noisy data compared to the standard approach based on vectors, and to recent continuous signal factorization approaches using splines or polynomials. We also show that our algorithm obtains state-of-the-art results in the domain of multicomponent nanostructures spectrum image unmixing