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A clustering framework within the sparse modeling and dictionary learning setting is introduced in this work. Instead of searching for the set of centroid that best fit the data, as in k-means type of approaches that model the data as distributions around discrete points, we optimize for a set of dictionaries, one for each cluster, for which the signals are best reconstructed in a sparse coding manner. Thereby, we are modeling the data as the of union of learned low dimensional subspaces, and data points associated to subspaces spanned by just a few atoms of the same learned dictionary are clustered together. Using learned dictionaries makes this method robust and well suited to handle large datasets. The proposed clustering algorithm uses a novel measurement for the quality of the sparse representation, inspired by the robustness of the ℓ1 regularization term in sparse coding. We first illustrate this measurement with examples on standard image and speech datasets in the supervised classification setting, showing with a simple approach its discriminative power and obtaining results comparable to the state-of-the-art. We then conclude with experiments for fully unsupervised clustering on extended standard datasets and texture images, obtaining excellent performance.
Date of Conference: 14-19 March 2010