The problem of transfer learning has recently been of great interest in a variety of machine learning applications. In this paper, we examine a new angle to the transfer learning problem, where we examine the problem of distance function learning. Specifically, we focus on the problem of how our knowledge of distance functions in one domain can be transferred to a new domain. A good semantic understanding of the feature space is critical in providing the domain specific understanding for setting up good distance functions. Unfortunately, not all domains have feature representations which are equally interpretable. For example, in some domains such as text, the semantics of the feature representation are clear, as a result of which it is easy for a domain expert to set up distance functions for specific kinds of semantics. In the case of image data, the features are semantically harder to interpret, and it is harder to set up distance functions, especially for particular semantic criteria. In this paper, we focus on the problem of transfer learning as a way to close the semantic gap between different domains, and show how to use correspondence information between two domains in order to set up distance functions for the semantically more challenging domain. Copyright © 2012 by the Society for Industrial and Applied Mathematics.