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Manifold regularization is a commonly used technique in semi-supervisedlearning. It enforces the classification rule to be smooth with respect to thedata-manifold. Here, we derive sample complexity bounds based onpseudo-dimension for models that add a convex data dependent regularizationterm to a supervised learning process, as is in particular done in Manifoldregularization. We then compare the bound for those semi-supervised methods topurely supervised methods, and discuss a setting in which the semi-supervisedmethod can only have a constant improvement, ignoring logarithmic terms. Byviewing Manifold regularization as a kernel method we then derive Rademacherbounds which allow for a distribution dependent analysis. Finally we illustratethat these bounds may be useful for choosing an appropriate manifoldregularization parameter in situations with very sparsely labeled data.

A Distribution Dependent and Independent Complexity Analysis of Manifold Regularization