One-Class Support Measure Machines for Group Anomaly Detection

Krikamol Muandet, Bernhard Schoelkopf
Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence, PMLR R11:549-558, 2013.

Abstract

We propose one-class support measure machines (OCSMMs) for group anomaly detection. Unlike traditional anomaly detection, OCSMMs aim at recognizing anomalous aggregate behaviors of data points. The OC- SMMs generalize well-known one-class support vector machines (OCSVMs) to a space of probability measures. By formulating the problem as quantile estimation on distributions, we can establish interesting connections to the OCSVMs and variable kernel density estimators (VKDEs) over the input space on which the distributions are defined, bridging the gap between large-margin methods and kernel density estimators. In particular, we show that various types of VKDEs can be considered as solutions to a class of regularization problems studied in this paper. Experiments on Sloan Digital Sky Survey dataset and High Energy Particle Physics dataset demonstrate the benefits of the proposed framework in real-world applications.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR11-muandet13a, title = {One-Class Support Measure Machines for Group Anomaly Detection}, author = {Muandet, Krikamol and Schoelkopf, Bernhard}, booktitle = {Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence}, pages = {549--558}, year = {2013}, editor = {Nicholson, Ann and Smyth, Padhraic}, volume = {R11}, series = {Proceedings of Machine Learning Research}, month = {12--14 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r11/main/assets/muandet13a/muandet13a.pdf}, url = {https://proceedings.mlr.press/r11/muandet13a.html}, abstract = {We propose one-class support measure machines (OCSMMs) for group anomaly detection. Unlike traditional anomaly detection, OCSMMs aim at recognizing anomalous aggregate behaviors of data points. The OC- SMMs generalize well-known one-class support vector machines (OCSVMs) to a space of probability measures. By formulating the problem as quantile estimation on distributions, we can establish interesting connections to the OCSVMs and variable kernel density estimators (VKDEs) over the input space on which the distributions are defined, bridging the gap between large-margin methods and kernel density estimators. In particular, we show that various types of VKDEs can be considered as solutions to a class of regularization problems studied in this paper. Experiments on Sloan Digital Sky Survey dataset and High Energy Particle Physics dataset demonstrate the benefits of the proposed framework in real-world applications.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T One-Class Support Measure Machines for Group Anomaly Detection %A Krikamol Muandet %A Bernhard Schoelkopf %B Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2013 %E Ann Nicholson %E Padhraic Smyth %F pmlr-vR11-muandet13a %I PMLR %P 549--558 %U https://proceedings.mlr.press/r11/muandet13a.html %V R11 %X We propose one-class support measure machines (OCSMMs) for group anomaly detection. Unlike traditional anomaly detection, OCSMMs aim at recognizing anomalous aggregate behaviors of data points. The OC- SMMs generalize well-known one-class support vector machines (OCSVMs) to a space of probability measures. By formulating the problem as quantile estimation on distributions, we can establish interesting connections to the OCSVMs and variable kernel density estimators (VKDEs) over the input space on which the distributions are defined, bridging the gap between large-margin methods and kernel density estimators. In particular, we show that various types of VKDEs can be considered as solutions to a class of regularization problems studied in this paper. Experiments on Sloan Digital Sky Survey dataset and High Energy Particle Physics dataset demonstrate the benefits of the proposed framework in real-world applications. %Z Reissued by PMLR on 04 October 2026.
APA
Muandet, K. & Schoelkopf, B.. (2013). One-Class Support Measure Machines for Group Anomaly Detection. Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R11:549-558 Available from https://proceedings.mlr.press/r11/muandet13a.html. Reissued by PMLR on 04 October 2026.

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