# Label-Informed Outlier Detection Based on Granule Density

arXiv: https://arxiv.org/abs/2512.18774 · HTML: https://mlsanity.com/paper/2512.18774/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 55 references that are in the map.
- First posted on arXiv 21 Dec 2025.

## Builds on (most cited first, 18 of 18)

- [Deep Semi-Supervised Anomaly Detection](https://mlsanity.com/paper/1906.02694/) (2019)
- [ADBench: Anomaly Detection Benchmark](https://mlsanity.com/paper/2206.09426/) (2022)
- [PyOD: A Python Toolbox for Scalable Outlier Detection](https://mlsanity.com/paper/1901.01588/) (2019)
- [Deep Anomaly Detection with Deviation Networks](https://mlsanity.com/paper/1911.08623/) (2019)
- [ECOD: Unsupervised Outlier Detection Using Empirical Cumulative Distribution Functions](https://mlsanity.com/paper/2201.00382/) (2022)
- [COPOD: Copula-Based Outlier Detection](https://mlsanity.com/paper/2009.09463/) (2020)
- [Deep Isolation Forest for Anomaly Detection](https://mlsanity.com/paper/2206.06602/) (2022)
- [Learning Representations of Ultrahigh-dimensional Data for Random Distance-based Outlier Detection](https://mlsanity.com/paper/1806.04808/) (2018)
- [Toward Supervised Anomaly Detection](https://mlsanity.com/paper/1401.6424/) (2014)
- [Deep Weakly-supervised Anomaly Detection](https://mlsanity.com/paper/1910.13601/) (2019)
- [XGBOD: Improving Supervised Outlier Detection with Unsupervised Representation Learning](https://mlsanity.com/paper/1912.00290/) (2019)
- [Toward Deep Supervised Anomaly Detection: Reinforcement Learning from Partially Labeled Anomaly Data](https://mlsanity.com/paper/2009.06847/) (2020)
- [Feature Encoding with AutoEncoders for Weakly-supervised Anomaly Detection](https://mlsanity.com/paper/2105.10500/) (2021)
- [LUNAR: Unifying Local Outlier Detection Methods via Graph Neural Networks](https://mlsanity.com/paper/2112.05355/) (2021)
- [Meta-AAD: Active Anomaly Detection with Deep Reinforcement Learning](https://mlsanity.com/paper/2009.07415/) (2020)
- [Weakly Supervised Anomaly Detection: A Survey](https://mlsanity.com/paper/2302.04549/) (2023)
- [Anomaly Detection by Leveraging Incomplete Anomalous Knowledge with Anomaly-Aware Bidirectional GANs](https://mlsanity.com/paper/2204.13335/) (2022)
- [ESAD: End-to-end Deep Semi-supervised Anomaly Detection](https://mlsanity.com/paper/2012.04905/) (2020)

## Abstract (arXiv)

Outlier detection, crucial for identifying unusual patterns with significant implications across numerous applications, has drawn considerable research interest. Existing semi-supervised methods typically treat data as purely numerical and} in a deterministic manner, thereby neglecting the heterogeneity and uncertainty inherent in complex, real-world datasets. This paper introduces a label-informed outlier detection method for heterogeneous data based on Granular Computing and Fuzzy Sets, namely Granule Density-based Outlier Factor (GDOF). Specifically, GDOF first employs label-informed fuzzy granulation to effectively represent various data types and develops granule density for precise density estimation. Subsequently, granule densities from individual attributes are integrated for outlier scoring by assessing attribute relevance with a limited number of labeled outliers. Experimental results on various real-world datasets show that GDOF stands out in detecting outliers in heterogeneous data with a minimal number of labeled outliers. The integration of Fuzzy Sets and Granular Computing in GDOF offers a practical framework for outlier detection in complex and diverse data types. All relevant datasets and source codes are publicly available for further research. This is the author's accepted manuscript of a paper published in IEEE Transactions on Fuzzy Systems. The final version is available at https://doi.org/10.1109/TFUZZ.2024.3514853