Metaphorical expressions are pervasive in natural language and pose a substantial challenge for computational semantics.The inherent compositionality of metaphor makes it an important test case for compositional distributional semantic models (CDSMs).This paper is the first to investigate whether metaphorical composition warrants a distinct treatment in the CDSM framework.We propose a method to learn metaphors as linear transformations in a vector space and find that, across a variety of semantic domains, explicitly modeling metaphor improves the resulting semantic representations.We then use these representations in a metaphor identification task, achieving a high performance of 0.82 in terms of F-score.