# Margin based Transductive Graph Cuts using Linear Programming

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K. Pelckmans,
J. Shawe-Taylor,
J.A.K. Suykens,
B. De Moor
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Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, PMLR 2:363-370, 2007.

#### Abstract

This paper studies the problem of inferring a partition (or a graph cut) of an undirected deterministic graph where the labels of some nodes are observed - thereby bridging a gap between graph theory and probabilistic inference techniques. Given a weighted graph, we focus on the rules of weighted neighbors to predict the label of a particular node. A maximum margin and maximal average margin based argument is used to prove a generalization bound, and is subsequently related to the classical MINCUT approach. From a practical perspective a simple and intuitive, but efficient convex formulation is constructed. This scheme can readily be implemented as a linear program which scales well till a few thousands of (labeled or unlabeled) data-points. The extremal case is studied where one observes only a single label, and this setting is related to the task of unsupervised clustering.

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