Abstract Lacking training examples is one of the main obstacles to learning systems. Transfer learning aims to extract and utilize useful information from related datasets and assists the current task effectively. Most existing methods restrict tasks connection on the same feature sets, or require aligned examples cross domains, even cannot take full advantage of the limited label information. In this paper, we focus on transferring between heterogeneous domains, i.e., those with different feature spaces, and propose the Metric Transporation on HEterogeneous REpresentations (M AP H ERE) approach. In particular, an asymmetric transformation map is first learned to compensate the crossdomain feature difference based on linkage relationship between objects; then the inner-domain discrepancy is further reduced with learned optimal transportation. Note that both source domain and cross-domain relationship are fully utilized in M A P H ERE , which helps improve target classification task a lot. Experiments on synthetic dataset validate the importance of the “metric facilitated” consideration, while results on real-world tasks show the superiority of the M AP H ERE approach.