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Pré-Publication, Document De Travail Année : 2023

Graph Cuts with Arbitrary Size Constraints Through Optimal Transport

Chakib Fettal
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  • PersonId : 1134902
Lazhar Labiod
Mohamed Nadif
  • Fonction : Auteur
  • PersonId : 990896

Résumé

Image Clustering is an important task in computer vision and machine learning in general, and new applications are constantly appearing. A common way of obtaining an image dataset partition is through graph cuts, which are also used as a component in more complex clustering paradigms such as subspace clustering. One drawback of classical min-cut algorithms is that they tend to produce small groups, which is why more balanced variants have risen, including normalized and ratio cuts. We believe, however, that with these variants the balance constraints are too restrictive for some applications (long-tailed clustering), while not being restrictive enough for others (when searching for perfectly balanced partitions), since the constraint is not hard. Here, we propose a new graph cut algorithm for partitioning with arbitrary size constraints. We formulate the graph cut problem as a constrained Gromov-Wasserstein problem, and our algorithm is slower than the classical spectral clustering algorithm by only a ratio of $\mathcal{O}(\log(n))$ while being more efficient in practice. We demonstrate the performance of our approach on several balanced and imbalanced (long-tail) datasets.
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Dates et versions

hal-03917041 , version 1 (31-12-2022)
hal-03917041 , version 2 (11-05-2023)
hal-03917041 , version 3 (30-08-2023)
hal-03917041 , version 4 (07-02-2024)

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  • HAL Id : hal-03917041 , version 2

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Chakib Fettal, Lazhar Labiod, Mohamed Nadif. Graph Cuts with Arbitrary Size Constraints Through Optimal Transport. 2023. ⟨hal-03917041v2⟩
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