In this paper, we present a novel method for the computation of compositionality within a distributional framework. The key idea is that compositionality is modeled as a multi-way interaction between latent factors, which are automatically constructed from corpus data. We use our method to model the composition of subject verb object triples. The method consists of two steps. First, we compute a latent factor model for nouns from standard co-occurrence data. Next, the latent factors are used to induce a latent model of three-way subject verb object interactions. Our model has been evaluated on a similarity task for transitive phrases, in which it exceeds the state of the art.