Revisiting clustering as matrix factorisation on the Stiefel manifold
Abstract
This paper studies clustering for possibly high dimensional data (e.g. images, time series, gene expression data, and many other settings), and rephrase it as low rank matrix estimation in the PAC-Bayesian framework. Our approach leverages the well known Burer-Monteiro factorisation strategy from large scale optimisation, in the context of low rank estimation. Moreover, our Burer-Monteiro factors are shown to lie on a Stiefel manifold. We propose a new generalized Bayesian estimator for this problem and prove novel prediction bounds for clustering. We also devise a componentwise Langevin sampler on the Stiefel manifold to compute this estimator.
Cite
@article{arxiv.1903.04479,
title = {Revisiting clustering as matrix factorisation on the Stiefel manifold},
author = {Stéphane Chrétien and Benjamin Guedj},
journal= {arXiv preprint arXiv:1903.04479},
year = {2021}
}
Comments
Accepted at the LOD 2020 Conference -- The Sixth International Conference on Machine Learning, Optimization, and Data Science