1. An apparatus comprising: a data classification system associated with a hybrid cloud comprising at least one private cloud and at least one public cloud; the data classification system comprising a data set classification model classifying data sets, a cloud classification model classifying the private and public clouds of the hybrid cloud into two or more different cloud classes, and a plurality of mapping policies each specifying a particular mapping between one or more classes of the data set classification model and one or more classes of the cloud classification model; wherein the data classification system is configured to classify a received data set using the data set classification model; wherein the data classification system further comprises a reasoner configured to determine a selected one of the mapping policies for the received data set, the reasoner comprising: a semantic ontology application programming interface; a model parser; a model updater; and a semantic learner; wherein the semantic ontology application programming interface provides programming access for adjusting one or more semantic ontologies utilized by the semantic learner; wherein the model parser extracts information from at least one of the data set classification model and the cloud classification model so as to make said information available to the semantic learner for use in performing one or more reasoning operations; wherein the model updater adjusts one or more characteristics of at least one of the data set classification model, the cloud classification model and one or more of the mapping policies responsive to feedback from the semantic learner; and wherein the semantic learner is configured to identify one or more additional relationship types that are not already captured in a current version of at least one of the data set classification model and the cloud classification model and to provide those relationship types to the model updater as part of said feedback; wherein the data classification system is further configured to determine for the received data set at least one cloud of the hybrid cloud to which the received data set should be directed for further processing based at least in part on a result of the classification of the received data set, the cloud classification model and the selected mapping policy; wherein the reasoner is further configured to migrate a given data set from a first cloud associated with a first one of the cloud classes to a second cloud associated with a second one of the cloud classes responsive to a change in at least one of the data set classification model, the cloud classification model and one or more of the mapping policies; and wherein the data classification system is implemented using at least one processing device comprising a processor coupled to a memory.