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Similarity graph-based max-flow and duality approaches for semi-supervised data classification and image segmentation

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Abstract

The max-flow problem entails the computation of a maximum feasible flow from a source to a sink through a network under constraints. Its connection to total variation presents an opportunity to apply the problem to machine learning tasks by incorporating a similarity graph-based setting. In this paper, we integrate max-flow and duality techniques, similarity graph-based frameworks, semi-supervised procedures, class size information and class homogeneity terms to derive three algorithms for machine learning tasks, such as classification, and image segmentation. The first algorithm involves similarity graph-based max-flow incorporating supervised constraints and class size information. The second method involves a duality approach and global minimization of similarity graph-based total variation problems incorporating class size information. The third algorithm involves graph-based convex optimization via max-flow techniques for image segmentation problems involving region parameters, in the case the latter is unknown. An important advantage of the methods is that they require only a small set of labeled samples for good accuracy, in part due to the integration of graph-based and semi-supervised techniques; this is an important advantage due to the scarcity of labeled data. Moreover, some of the proposed algorithms are based on global minimization, and are also able to incorporate class size information, which often improves performance. In addition, the methods perform well on both large and small data sets, the latter of which can result in poor performances for learning methods due to a decreased ability to learn from observed data. The proposed methods are validated using benchmark data sets and are compared favorably to recent methods.

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Data availibility statement

The links to all the data sets analyzed in this paper are included in this paper via citations, and the data is also available at the repository at https://github.com/kmerkurev/Data.

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    Ekaterina Merkurjev

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Merkurjev, E. Similarity graph-based max-flow and duality approaches for semi-supervised data classification and image segmentation. Int. J. Mach. Learn. & Cyber. 14, 4285–4310 (2023). https://doi.org/10.1007/s13042-023-01894-7

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