In this paper we propose to combine two powerful ideas, boosting and manifold learning. On the one hand, we improve ADABOOST by incorporating knowledge on the structure of the data into base classifier design and selection. On the other hand, we use ADABOOST's efficient learning mechanism to significantly improve supervised and semi-supervised algorithms proposed in the context of manifold learning. Beside the specific manifold-based penalization, the resulting algorithm also accommodates the boosting of a large family of regularized learning algorithms.