We present a probabilistic subspace clustering approach that is capable of rapidly clustering very large signal collections. Each signal is represented by a sparse combination of basis elements (atoms), which form the columns of a dictionary matrix. The set of sparse representations is utilized to derive the co-occurrences matrix of atoms and signals, which is modeled as emerging from a mixture model. The components of the mixture model are obtained via a non-negative matrix factorization (NNMF) of the co-occurrences matrix, and the subspace of each signal is estimated according to a maximum-likelihood (ML) criterion. Performance evaluation demonstrate comparable clustering accuracies to state-of-the-art at a fraction of the computational load.