# One-Class Support Measure Machines for Group Anomaly Detection

arXiv: https://arxiv.org/abs/1303.0309 · HTML: https://mlsanity.com/paper/1303.0309/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2013.

## Built on by (most cited first, 12 of 12)

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- [gen2Out: Detecting and Ranking Generalized Anomalies](https://mlsanity.com/paper/2109.02704/) (2021)
- [New Methods and Datasets for Group Anomaly Detection From Fundamental Physics](https://mlsanity.com/paper/2107.02821/) (2021)
- [Novelty Detection on Radio Astronomy Data using Signatures](https://mlsanity.com/paper/2402.14892/) (2024)
- [Generalized Identifiability Bounds for Mixture Models with Grouped Samples](https://mlsanity.com/paper/2207.11164/) (2022)
- [Tractable Computation of Expected Kernels](https://mlsanity.com/paper/2102.10562/) (2021)
- [Breaking the curse of dimensionality with Isolation Kernel](https://mlsanity.com/paper/2109.14198/) (2021)
- [GADformer: A Transparent Transformer Model for Group Anomaly Detection on Trajectories](https://mlsanity.com/paper/2303.09841/) (2023)
- [Kernel Mean Estimation by Marginalized Corrupted Distributions](https://mlsanity.com/paper/2107.04855/) (2021)
- [Non-Linear Spectral Dimensionality Reduction Under Uncertainty](https://mlsanity.com/paper/2202.04678/) (2022)
- [Out-of-Distribution Detection using Maximum Entropy Coding](https://mlsanity.com/paper/2404.17023/) (2024)
- [Finite-Sample Unbiased Variance of MMD under Unbalanced Sampling: Exact Estimation and Quasi-Linear Computation](https://mlsanity.com/paper/2601.13874/) (2026)

## Abstract (arXiv)

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.