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We propose sparse representation and dictionary learning algorithms for dictionaries whose atoms are characterized by Gaussian probability distributions around some central atoms. This extension of the space covered by the atoms permits a better characterization of localized features of the signals. The representations are computed by trading-off representation error and the probability of the actual atoms used in the representation. We propose two types of algorithms: a greedy one, similar in spirit with Orthogonal Matching Pursuit, and one based on L1-regularization. We apply our new algorithms to unsupervised anomaly detection, where the representation error is used as anomaly score. The flexibility of our approach appears to improve more the representations of the many normal signals than those of the few outliers, at least for an anomaly type called dependency, thus improving the detection quality. Comparison with both standard dictionary learning algorithms and established anomaly detection methods is favorable.

Sparse Representation with Gaussian Atoms and its use in Anomaly Detection