Non-compositionality of multiword expressions is an intriguing problem that can be the source of error in a variety of NLP tasks such as language generation, machine translation and word sense disambiguation. We present methods of non-compositionality detection for English noun compounds using the unsupervised learning of a semantic composition function. Compounds which are not well modeled by the learned semantic composition function are considered noncompositional. We explore a range of distributional vector-space models for semantic composition, empirically evaluate these models, and propose additional methods which improve results further. We show that a complex function such as polynomial projection can learn semantic composition and identify non-compositionality in an unsupervised way, beating all other baselines ranging from simple to complex. We show that enforcing sparsity is a useful regularizer in learning complex composition functions. We show further improvements by training a decomposition function in addition to the composition function. Finally, we propose an EM algorithm over latent compositionality annotations that also improves the performance.