# Explaining Anomalies in Groups with Characterizing Subspace Rules

arXiv: https://arxiv.org/abs/1708.05929 · HTML: https://mlsanity.com/paper/1708.05929/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Aug 2017.

## Built on by (most cited first, 13 of 13)

- [A Survey on Explainable Anomaly Detection](https://mlsanity.com/paper/2210.06959/) (2022)
- [Root Cause Analysis of Outliers with Missing Structural Knowledge](https://mlsanity.com/paper/2406.05014/) (2024)
- [On the Detection of Reviewer-Author Collusion Rings From Paper Bidding](https://mlsanity.com/paper/2402.07860/) (2024)
- [Towards Reliable Rare Category Analysis on Graphs via Individual Calibration](https://mlsanity.com/paper/2307.09858/) (2023)
- [Framing Algorithmic Recourse for Anomaly Detection](https://mlsanity.com/paper/2206.14384/) (2022)
- [D.MCA: Outlier Detection with Explicit Micro-Cluster Assignments](https://mlsanity.com/paper/2210.08212/) (2022)
- [From Explanation to Action: An End-to-End Human-in-the-loop Framework for Anomaly Reasoning and Management](https://mlsanity.com/paper/2304.03368/) (2023)
- [A Probabilistic Transformation of Distance-Based Outliers](https://mlsanity.com/paper/2305.09446/) (2023)
- [A Feature Engineering Approach for Business Impact-Oriented Failure Detection in Distributed Instant Payment Systems](https://mlsanity.com/paper/2510.21710/) (2025)
- [Anomaly Mining -- Past, Present and Future](https://mlsanity.com/paper/2105.10077/) (2021)
- [On Predictive Explanation of Data Anomalies](https://mlsanity.com/paper/2110.09467/) (2021)
- [Structured Prompt Optimization Meets Reinforcement Learning for Global and Local Interpretability over Complex Text](https://mlsanity.com/paper/2605.29076/) (2026)
- [Beyond Conditional Independence: Root Cause Analysis with Deep Causal Models](https://mlsanity.com/paper/2609.36771/) (2026)

## Abstract (arXiv)

Anomaly detection has numerous applications and has been studied vastly. We consider a complementary problem that has a much sparser literature: anomaly description. Interpretation of anomalies is crucial for practitioners for sense-making, troubleshooting, and planning actions. To this end, we present a new approach called x-PACS (for eXplaining Patterns of Anomalies with Characterizing Subspaces), which "reverse-engineers" the known anomalies by identifying (1) the groups (or patterns) that they form, and (2) the characterizing subspace and feature rules that separate each anomalous pattern from normal instances. Explaining anomalies in groups not only saves analyst time and gives insight into various types of anomalies, but also draws attention to potentially critical, repeating anomalies. In developing x-PACS, we first construct a desiderata for the anomaly description problem. From a descriptive data mining perspective, our method exhibits five desired properties in our desiderata. Namely, it can unearth anomalous patterns (i) of multiple different types, (ii) hidden in arbitrary subspaces of a high dimensional space, (iii) interpretable by the analysts, (iv) different from normal patterns of the data, and finally (v) succinct, providing the shortest data description. Furthermore, x-PACS is highly parallelizable and scales linearly in terms of data size. No existing work on anomaly description satisfies all of these properties simultaneously. While not our primary goal, the anomalous patterns we find serve as interpretable "signatures" and can be used for detection. We show the effectiveness of x-PACS in explanation as well as detection on real-world datasets as compared to state-of-the-art.