# Isolation Distributional Kernel: A New Tool for Point & Group Anomaly Detection

arXiv: https://arxiv.org/abs/2009.12196 · HTML: https://mlsanity.com/paper/2009.12196/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Sep 2020.

## Built on by (most cited first, 7 of 7)

- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Graph Spatiotemporal Process for Multivariate Time Series Anomaly Detection with Missing Values](https://mlsanity.com/paper/2401.05800/) (2024)
- [Anomaly Detection Based on Isolation Mechanisms: A Survey](https://mlsanity.com/paper/2403.10802/) (2024)
- [Detecting Change Intervals with Isolation Distributional Kernel](https://mlsanity.com/paper/2212.14630/) (2022)
- [Isolation forests: looking beyond tree depth](https://mlsanity.com/paper/2111.11639/) (2021)
- [An Online Automatic Modulation Classification Scheme Based on Isolation Distributional Kernel](https://mlsanity.com/paper/2410.02750/) (2024)
- [A New Framework for Explainable Rare Cell Identification in Single-Cell Transcriptomics Data](https://mlsanity.com/paper/2601.01358/) (2026)

## Abstract (arXiv)

We introduce Isolation Distributional Kernel as a new way to measure the similarity between two distributions. Existing approaches based on kernel mean embedding, which convert a point kernel to a distributional kernel, have two key issues: the point kernel employed has a feature map with intractable dimensionality; and it is em data independent. This paper shows that Isolation Distributional Kernel (IDK), which is based on a em data dependent point kernel, addresses both key issues. We demonstrate IDK's efficacy and efficiency as a new tool for kernel based anomaly detection for both point and group anomalies. Without explicit learning, using IDK alone outperforms existing kernel based point anomaly detector OCSVM and other kernel mean embedding methods that rely on Gaussian kernel. For group anomaly detection,we introduce an IDK based detector called IDK2. It reformulates the problem of group anomaly detection in input space into the problem of point anomaly detection in Hilbert space, without the need for learning. IDK2 runs orders of magnitude faster than group anomaly detector OCSMM.We reveal for the first time that an effective kernel based anomaly detector based on kernel mean embedding must employ a characteristic kernel which is data dependent.