An analysis of graph cut size for transductive learning

Abstract

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).

Learning Unknown Graphs

“…This approach guarantees that the number of mistakes is bounded by a quantity that depends linearly on the cutsize Φ G (y). Further results involving the prediction of node labels in graphs with known structure include [5,6,7,8,9,10,11,12,13,14]. Since all these papers assume knowledge of the entire graph in advance, the techniques proposed for transductive binary prediction do not have any mechanism for guiding the exploration of the graph, hence they do not work well on the exploration/prediction problem studied in this work.…”

Large margin vs. large volume in transductive learning

“…The maximalmargin principle motivated the well known transductive SVM (TSVM) approach. Other prior assignment approaches using compression, clustering and graph cuts are discussed in (Derbeko et al 2004) and (Hanneke 2006).…”

Transductive Rademacher Complexity and Its Applications

“…Effective applications of the general bounds mentioned above to particular algorithms or "learning principles" is not automatic. In the case of the PAC-Bayesian bounds several such successful applications were presented in terms of appropriate "priors" that promote various structural properties of the data (see, e.g., Derbeko et al, 2004;El-Yaniv & Gerzon, 2005;Hanneke, 2006). Ad-hoc bounds for particular algorithms were developed by and by Johnson and Zhang (2007).…”