In this paper we introduce a novel approach to manifold alignment, based on Procrustes analysis. Our approach di®ers from \semi- supervised alignment" in that it results in a mapping that is de¯ned everywhere { when used with a suitable dimensionality reduction method { rather than just on the training data points. We describe and evaluate our approach both theoretically and experimen- tally, providing results showing useful knowl- edge transfer from one domain to another. Novel applications of our method including cross-lingual information retrieval and trans- fer learning in Markov decision processes are presented.