This study explores sparse representation techniques tailored for multivariate extremes and their application in anomaly detection. Multivariate extremes, characterized by rare events occurring jointly across multiple dimensions, pose significant challenges for traditional anomaly detection methods. Sparse representation approaches offer a promising solution by identifying a parsimonious set of extreme features that capture the most salient aspects of multivariate outliers. Leveraging techniques such as sparse coding, dictionary learning, and compressed sensing, sparse representation methods enable efficient representation and detection of anomalies in high-dimensional datasets. This paper reviews recent advances in sparse representation techniques for multivariate extremes and discusses their practical applications in anomaly detection across various domains, including finance, cybersecurity, and environmental monitoring.

Sparse representation, multivariate extremes, anomaly detection

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