Matrix and tensor factorizations are widely applied in Data Science for dimensionality and noise reduction as well as for feature extraction. Often, additional constraints are imposed on the factors in order to improve the uniqueness and interpretability of the results. We consider several specific factorization formats with smooth and nonsmooth constraints that can be computed using techniques from Riemannian optimization. For this, existing methods need to be adapted according to the problem at hand. Furthermore, we apply our methods also for Data Fusion, where several data sets are factorized simultaneously.
Dr. Max Pfeffer is a Junior Professor of Mathematics at Georg-August-Universität Göttingen since April 2023. Prior to this, he held research and academic positions at SimulaMet (Oslo), Technische Universität Chemnitz, Johannes Gutenberg University Mainz, Universität Leipzig, and the Max Planck Institute for Mathematics in the Sciences in Leipzig. He completed his PhD in Mathematics at TU Berlin in 2018, where he also earned his M.Sc. and B.Sc. degrees. His research interest is in tensors, Riemannian optimization and applications.