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We describe a data-driven algorithm for automatically identifying repeated patterns in music which analyzes a feature matrix using shift-invariant probabilistic latent component analysis. We utilize sparsity constraints to automatically identify the number of patterns and their lengths, parameters that would normally need to be fixed in advance, as well as to control the structure of the decomposition. The proposed analysis is applied to beat-synchronous chromagrams in order to concurrently extract recurrent harmonic motifs and their locations within a song. We demonstrate how the analysis can be used to accurately identify riffs in popular music and explore the relationship between the derived parameters and a song's underlying metrical structure. Finally, we show how this analysis can be used for long-term music structure segmentation, resulting in an algorithm that is competitive with other state-of-the-art segmentation algorithms based on hidden Markov models and self similarity matrices.