# Random Coordinate Descent Methods for Minimizing Decomposable Submodular Functions

arXiv: https://arxiv.org/abs/1502.02643 · HTML: https://mlsanity.com/paper/1502.02643/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Feb 2015.

## Built on by (most cited first, 4 of 4)

- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [Decomposable Submodular Function Minimization via Maximum Flow](https://mlsanity.com/paper/2103.03868/) (2021)
- [Approximate Decomposable Submodular Function Minimization for Cardinality-Based Components](https://mlsanity.com/paper/2110.14859/) (2021)
- [Hypergraphs with Edge-Dependent Vertex Weights: p-Laplacians and Spectral Clustering](https://mlsanity.com/paper/2208.07457/) (2022)

## Abstract (arXiv)

Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have high running times and are unsuitable for large-scale problems. Recent work have used convex optimization techniques to obtain very practical algorithms for minimizing functions that are sums of ``simple" functions. In this paper, we use random coordinate descent methods to obtain algorithms with faster linear convergence rates and cheaper iteration costs. Compared to alternating projection methods, our algorithms do not rely on full-dimensional vector operations and they converge in significantly fewer iterations.