Cut-Pursuit Algorithm for Regularizing Nonsmooth Functionals with Graph Total Variation

Hugo Raguet, Loic Landrieu
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:4247-4256, 2018.

Abstract

We present an extension of the cut-pursuit algorithm, introduced by Landrieu and Obozinski (2017), to the graph total-variation regularization of functions with a separable nondifferentiable part. We propose a modified algorithmic scheme as well as adapted proofs of convergence. We also present a heuristic approach for handling the cases in which the values associated to each vertex of the graph are multidimensional. The performance of our algorithm, which we demonstrate on difficult, ill-conditioned large-scale inverse and learning problems, is such that it may in practice extend the scope of application of the total-variation regularization.

Cite this Paper

BibTeX
@InProceedings{pmlr-v80-raguet18a, title = {Cut-Pursuit Algorithm for Regularizing Nonsmooth Functionals with Graph Total Variation}, author = {Raguet, Hugo and Landrieu, Loic}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {4247--4256}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/raguet18a/raguet18a.pdf}, url = {https://proceedings.mlr.press/v80/raguet18a.html}, abstract = {We present an extension of the cut-pursuit algorithm, introduced by Landrieu and Obozinski (2017), to the graph total-variation regularization of functions with a separable nondifferentiable part. We propose a modified algorithmic scheme as well as adapted proofs of convergence. We also present a heuristic approach for handling the cases in which the values associated to each vertex of the graph are multidimensional. The performance of our algorithm, which we demonstrate on difficult, ill-conditioned large-scale inverse and learning problems, is such that it may in practice extend the scope of application of the total-variation regularization.} }
Endnote
%0 Conference Paper %T Cut-Pursuit Algorithm for Regularizing Nonsmooth Functionals with Graph Total Variation %A Hugo Raguet %A Loic Landrieu %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-raguet18a %I PMLR %P 4247--4256 %U https://proceedings.mlr.press/v80/raguet18a.html %V 80 %X We present an extension of the cut-pursuit algorithm, introduced by Landrieu and Obozinski (2017), to the graph total-variation regularization of functions with a separable nondifferentiable part. We propose a modified algorithmic scheme as well as adapted proofs of convergence. We also present a heuristic approach for handling the cases in which the values associated to each vertex of the graph are multidimensional. The performance of our algorithm, which we demonstrate on difficult, ill-conditioned large-scale inverse and learning problems, is such that it may in practice extend the scope of application of the total-variation regularization.
APA
Raguet, H. & Landrieu, L.. (2018). Cut-Pursuit Algorithm for Regularizing Nonsmooth Functionals with Graph Total Variation. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:4247-4256 Available from https://proceedings.mlr.press/v80/raguet18a.html.

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