We study the problem of learning a classification task in which only a dissimilarity function of the objects is accessible. That is, data are not represented by feature vectors but in terms of their pairwise dissimilarities. We investigate the sufficient conditions for dissimilarity functions to allow building accurate classifiers. Our results have the advantages that they apply to unbounded dissimilarities and are invariant to order-preserving transformations. The theory immediately suggests a learning paradigm: construct an ensemble of decision stumps each depends on a pair of examples, then find a convex combination of them to achieve a large margin. We next develop a practical algorithm called Dissimilarity based Boosting (DBoost) for learning with dissimilarity functions under the theoretical guidance. Experimental results demonstrate that DBoost compares favorably with several existing approaches on a variety of databases and under different conditions. 1.