An analysis of graph cut size for transductive learning

I consider the setting of transductive learning of vertex labels in graphs, in which a graph with n vertices is sampled according to some unknown distribution; there is a true labeling of the vertices such that each vertex is assigned to exactly one of k classes, but the labels of only some (random) subset of the vertices are revealed to the learner. The task is then to find a labeling of the remaining (unlabeled) vertices that agrees as much as possible with the true labeling. Several existing algorithms are based on the assumption that adjacent vertices are usually labeled the same. In order to better understand algorithms based on this assumption, I derive data-dependent bounds on the fraction of mislabeled vertices, based on the number (or total weight) of edges between vertices differing in predicted label (i.e., the size of the cut).

• Type: Conference
• Year: 2006
• Where: ICML
• Authors: Steve Hanneke
• Keywords: Adjacent Vertices, ICML 2006, Machine Learning, Several Existing Algorithms, True Labeling