# A Greedy Strategy for Graph Cut

arXiv: https://arxiv.org/abs/2412.20035 · HTML: https://mlsanity.com/paper/2412.20035/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 32 references that are in the map.
- First posted on arXiv 28 Dec 2024.

## Builds on (most cited first, 5 of 5)

- [Efficient Parameter-free Clustering Using First Neighbor Relations](https://mlsanity.com/paper/1902.11266/) (2019)
- [Ultra-Scalable Spectral Clustering and Ensemble Clustering](https://mlsanity.com/paper/1903.01057/) (2019)
- [Clustering Millions of Faces by Identity](https://mlsanity.com/paper/1604.00989/) (2016)
- [Approximate Hierarchical Clustering via Sparsest Cut and Spreading Metrics](https://mlsanity.com/paper/1609.09548/) (2016)
- [Hierarchical Clustering better than Average-Linkage](https://mlsanity.com/paper/1808.02227/) (2018)

## Abstract (arXiv)

We propose a Greedy strategy to solve the problem of Graph Cut, called GGC. It starts from the state where each data sample is regarded as a cluster and dynamically merges the two clusters which reduces the value of the global objective function the most until the required number of clusters is obtained, and the monotonicity of the sequence of objective function values is proved. To reduce the computational complexity of GGC, only mergers between clusters and their neighbors are considered. Therefore, GGC has a nearly linear computational complexity with respect to the number of samples. Also, unlike other algorithms, due to the greedy strategy, the solution of the proposed algorithm is unique. In other words, its performance is not affected by randomness. We apply the proposed method to solve the problem of normalized cut which is a widely concerned graph cut problem. Extensive experiments show that better solutions can often be achieved compared to the traditional two-stage optimization algorithm (eigendecomposition + k-means), on the normalized cut problem. In addition, the performance of GGC also has advantages compared to several state-of-the-art clustering algorithms.