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This paper describes a novel music similarity calculation method that is based on the instrumentation of music pieces. The approach taken here is based on the idea that sparse representations of musical audio signals are a rich source of information regarding the elements that constitute the observed spectra. We propose a method to extract feature vectors based on sparse representations and use these to calculate a similarity measure between songs. To train a dictionary for sparse representations from a large amount of training data, a novel dictionary-initialization method based on agglomerative clustering is proposed. An objective evaluation shows that the new features improve the performance of similarity calculation compared to the standard mel-frequency cepstral coefficients features.