Seminar Details
2025-06-17 (14h) : Matrix Factorization and Approximation of Nonnegative Rank Two
At Euler building (room A.002)
Speaker :
Van Dooren, Paul
Abstract :
We consider the problem of finding the best nonnegative rank two approxi-
mation of an arbitrary nonnegative matrix. We first provide a parametrization
of all possible nonnegative factorizations of a nonnegative matrix of rank 2. We
then use this result to construct a suboptimal, but cheaply computable, solution
of the nonnegative rank 2 approximation problem for an arbitrary nonnegative
matrix input; this can then be used as a starting point for the Alternating Least
Squares method, resulting in both an improved computational complexity and
an enhanced output quality. We provide numerical experiments to support these
claims. We also look at some variants of the problem, including symmetry con-
straints and three-way factorizations.
This is joint work with Etna Lindy and Vanni Noferini (Aalto University).