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Anomaly detection using the Poisson process limit for extremes

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Abstract
Anomaly detection starts from a model of normal behavior and classifies departures from this model as anomalies. This paper introduces a statistical non-parametric approach for anomaly detection that is based on a multivariate extension of the Poisson point process model for univariate extremes. The method is demonstrated on both a synthetic and a real-world data set, the latter being an unbalanced data set of acceleration data collected from movements of 7 pediatric patients suffering from epilepsy that is previously studied in [1]. The positive predictive values could be improved with an increase up to 12.9% (and a mean of 7%) while the sensitivity scores stayed unaltered. The proposed method was also shown to outperform an one-class SVM classifier. Because the Poisson point process model of extremes is able to combine information on the number of excesses over a fixed threshold with that on the excess values, a powerful model to detect anomalies is obtained that can be of high value in many application.
Keywords
anomaly detection, extreme value statistics, Poisson point process, unbalanced data, semi-supervised, NOVELTY DETECTION, STATISTICS, SUPPORT

Citation

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Chicago
Luca, Stijn, Peter Karsmakers, and Bart Vanrumste. 2014. “Anomaly Detection Using the Poisson Process Limit for Extremes.” In IEEE International Conference on Data Mining, ed. R Kumar, H Toivonen, J Pei, JZ Huang, and X Wu, 370–379. New York, NY, USA: IEEE.
APA
Luca, S., Karsmakers, P., & Vanrumste, B. (2014). Anomaly detection using the Poisson process limit for extremes. In R. Kumar, H. Toivonen, J. Pei, J. Huang, & X. Wu (Eds.), IEEE International Conference on Data Mining (pp. 370–379). Presented at the 14th IEEE International conference on Data Mining (IEEE ICDM), New York, NY, USA: IEEE.
Vancouver
1.
Luca S, Karsmakers P, Vanrumste B. Anomaly detection using the Poisson process limit for extremes. In: Kumar R, Toivonen H, Pei J, Huang J, Wu X, editors. IEEE International Conference on Data Mining. New York, NY, USA: IEEE; 2014. p. 370–9.
MLA
Luca, Stijn, Peter Karsmakers, and Bart Vanrumste. “Anomaly Detection Using the Poisson Process Limit for Extremes.” IEEE International Conference on Data Mining. Ed. R Kumar et al. New York, NY, USA: IEEE, 2014. 370–379. Print.
@inproceedings{8581160,
  abstract     = {Anomaly detection starts from a model of normal behavior and classifies departures from this model as anomalies. This paper introduces a statistical non-parametric approach for anomaly detection that is based on a multivariate extension of the Poisson point process model for univariate extremes. The method is demonstrated on both a synthetic and a real-world data set, the latter being an unbalanced data set of acceleration data collected from movements of 7 pediatric patients suffering from epilepsy that is previously studied in [1]. The positive predictive values could be improved with an increase up to 12.9\% (and a mean of 7\%) while the sensitivity scores stayed unaltered. The proposed method was also shown to outperform an one-class SVM classifier. Because the Poisson point process model of extremes is able to combine information on the number of excesses over a fixed threshold with that on the excess values, a powerful model to detect anomalies is obtained that can be of high value in many application.},
  author       = {Luca, Stijn and Karsmakers, Peter and Vanrumste, Bart},
  booktitle    = {IEEE International Conference on Data Mining},
  editor       = {Kumar, R and Toivonen, H and Pei, J and Huang, JZ and Wu, X},
  isbn         = {9781479943029},
  issn         = {1550-4786},
  language     = {eng},
  location     = {Shenzhen, PR China},
  pages        = {370--379},
  publisher    = {IEEE},
  title        = {Anomaly detection using the Poisson process limit for extremes},
  url          = {http://dx.doi.org/10.1109/icdm.2014.12},
  year         = {2014},
}

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