Clustering on Dynamic Graphs Based on Total Variation

Berger, Peter M.; Dittrich, Thomas; Matz, Gerald

doi:10.1109/sampta45681.2019.9030924

Cited by 2 publications

(1 citation statement)

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“…Berger et al [4] considered the problem of semisupervised clustering for multiple (more than two) classes, in which the clustering task is formulated as a convex optimization problem with an l 1 -norm regularization term. To solve the problem of clustering on dynamic graphs, Berger, Dittrich, and Matz [5] presented a low-complexity ADMM-based algorithm performing only local cluster updates via semi-supervised TV minimization. Motivated by signed cut minimization, Dittrich and Matz [10] proposed an optimization problem that minimizes the total variation of the cluster labels subject to constraints on the cluster size, augmented with a regularization that prevents clusters consisting of isolated nodes.…”

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The truncated variational model for image labeling and graph partitioning

Li,

Yang,

Yin

et al. 2024

IPI

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Image labeling and graph partitioning aim to divide a set of pixels or vertices into a specific number of meaningful groups. In this paper, we propose effective truncated regularization methods for both image labeling and graph partitioning problems. More specifically, we present optimization models for piecewise constant and piecewise smooth image labeling that minimize the truncation of different potential functions. The efficient alternating direction method of multipliers based algorithm is put forward for solving these models, where all subproblems can be solved by the closed-form solution or fast Fourier transform. Moreover, we propose a semi-supervised graph partitioning model based on truncated regularization under the definition of the graph, which is solved by the proximal gradient method. The efficiency of the proposed methods is demonstrated through labeling results on synthetic and real images and semi-supervised partitioning results on graph data.

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confidence: 99%