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In this paper we present a novel approach to describe sound mixtures which is based on a geometric viewpoint. In this approach we extend the idea of a nearest-neighbor representation to address the case of superimposed sources. We show that in order to account for mixing effects we need to perform a search for nearest-subspaces, as opposed to nearest-neighbors. In order to reduce the excessive computational complexity of this search we present an efficient algorithm to solve this problem which amounts to a sparse coding approach. We demonstrate the efficacy of this algorithm by using it to separate mixtures of speech.