Finding mappings between compatible ontologies is an important but difficult open problem. Instance-based methods for solving this problem have the advantage of focusing on the most active parts of the ontologies and reflect concept semantics as they are actually being used. However such methods have not at present been widely investigated in ontology mapping, compared to linguistic and structural techniques. Furthermore, previous instance-based mapping techniques were only applicable to cases where a substantial set of instances was available that was doubly annotated with both vocabularies. In this paper we approach the mapping problem as a classification problem based on the similarity between instances of concepts. This has the advantage that no doubly annotated instances are required, so that the method can be applied to any two corpora annotated with their own vocabularies. We evaluate the resulting classifiers on two real-world use cases, one with homogeneous and one with heterogeneous instances. The results illustrate the efficiency and generality of this method.