Chrétien, S;
Guedj, B;
(2021)
Revisiting clustering as matrix factorisation on the Stiefel manifold.
In: Nicosia, G and Ojha, V and La Malfa, E and Jansen, G and Sciacca, V and Pardalos, P and Giuffrida, G and Umeton, R, (eds.)
Machine Learning, Optimization, and Data Science. LOD 2020.
(pp. pp. 1-12).
Springer: Cham, Switzerland.
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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 BurerMonteiro 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.
| Type: | Proceedings paper |
|---|---|
| Title: | Revisiting clustering as matrix factorisation on the Stiefel manifold |
| Event: | Sixth International Conference on Machine Learning, Optimization, and Data Science |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/978-3-030-64583-0_1 |
| Publisher version: | http://dx.doi.org/10.1007/978-3-030-64583-0_1 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Clustering, concentration inequalities, non-negative matrix factorisation, Gaussian mixtures, PAC-Bayes, optimisation on manifolds. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10109702 |
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