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

arXiv: https://arxiv.org/abs/1802.04383 · HTML: https://mlsanity.com/paper/1802.04383/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2018.

## Built on by (most cited first, 2 of 2)

- [Graphmax for Text Generation](https://mlsanity.com/paper/2101.00153/) (2021)
- [Variational models for signal processing with Graph Neural Networks](https://mlsanity.com/paper/2103.16337/) (2021)

## Abstract (arXiv)

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.