One-Class Support Measure Machines for Group Anomaly Detection

TL;DR

This paper introduces one-class support measure machines (OCSMMs) for detecting anomalies at the group level by extending one-class SVMs to probability measure spaces, connecting margin-based methods with kernel density estimation.

Contribution

The paper develops OCSMMs that generalize OC SVMs to probability measures, linking large-margin methods with kernel density estimators for group anomaly detection.

Findings

Effective in real-world datasets

Bridges gap between margin methods and density estimation

Demonstrates improved anomaly detection performance

Abstract

We propose one-class support measure machines (OCSMMs) for group anomaly detection which aims at recognizing anomalous aggregate behaviors of data points. The OCSMMs 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 an interesting connection 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.