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# Relating Function Class Complexity and Cluster Structure in the Function Domain with Applications to Transduction

*Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics*, PMLR 9:437-444, 2010.

#### Abstract

We relate function class complexity to structure in the function domain. This facilitates risk analysis relative to cluster structure in the input space which is particularly effective in semi-supervised learning. In particular we quantify the complexity of function classes defined over a graph in terms of the graph structure.