Tensor completion using geodesics on Segre manifolds
Differential Geometry
2024-07-02 v1 Information Retrieval
Machine Learning
Abstract
We propose a Riemannian conjugate gradient (CG) optimization method for finding low rank approximations of incomplete tensors. Our main contribution consists of an explicit expression of the geodesics on the Segre manifold. These are exploited in our algorithm to perform the retractions. We apply our method to movie rating predictions in a recommender system for the MovieLens dataset, and identification of pure fluorophores via fluorescent spectroscopy with missing data. In this last application, we recover the tensor decomposition from less than of the data.
Cite
@article{arxiv.2108.00735,
title = {Tensor completion using geodesics on Segre manifolds},
author = {Lars Swijsen and Joeri Van der Veken and Nick Vannieuwenhoven},
journal= {arXiv preprint arXiv:2108.00735},
year = {2024}
}