# Clustering with Outlier Removal

arXiv: https://arxiv.org/abs/1801.01899 · HTML: https://mlsanity.com/paper/1801.01899/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jan 2018.

## Built on by (most cited first, 10 of 10)

- [A Comprehensive Survey on Deep Clustering: Taxonomy, Challenges, and Future Directions](https://mlsanity.com/paper/2206.07579/) (2022)
- [Deep Clustering based Fair Outlier Detection](https://mlsanity.com/paper/2106.05127/) (2021)
- [Is Simple Uniform Sampling Effective for Center-Based Clustering with Outliers: When and Why?](https://mlsanity.com/paper/2103.00558/) (2021)
- [Cluster Purging: Efficient Outlier Detection based on Rate-Distortion Theory](https://mlsanity.com/paper/2302.11234/) (2023)
- [Clustered Hierarchical Anomaly and Outlier Detection Algorithms](https://mlsanity.com/paper/2103.11774/) (2021)
- [IPOF: An Extremely and Excitingly Simple Outlier Detection Booster via Infinite Propagation](https://mlsanity.com/paper/2108.00360/) (2021)
- [SSDBCODI: Semi-Supervised Density-Based Clustering with Outliers Detection Integrated](https://mlsanity.com/paper/2208.05561/) (2022)
- [Fast maneuver recovery from aerial observation: trajectory clustering and outliers rejection](https://mlsanity.com/paper/2407.02863/) (2024)
- [Outlier detection in mixed-attribute data: a semi-supervised approach with fuzzy approximations and relative entropy](https://mlsanity.com/paper/2512.18978/) (2025)
- [Seed-Guided Semi-Supervised Clustering by A-Contrario Anomaly Detection](https://mlsanity.com/paper/2606.18833/) (2026)

## Abstract (arXiv)

Cluster analysis and outlier detection are strongly coupled tasks in data mining area. Cluster structure can be easily destroyed by few outliers; on the contrary, outliers are defined by the concept of cluster, which are recognized as the points belonging to none of the clusters. Unfortunately, most existing studies do not notice the coupled relationship between these two task and handle them separately. In light of this, we consider the joint cluster analysis and outlier detection problem, and propose the Clustering with Outlier Removal (COR) algorithm. Generally speaking, the original space is transformed into the binary space via generating basic partitions in order to define clusters. Then an objective function based Holoentropy is designed to enhance the compactness of each cluster with a few outliers removed. With further analyses on the objective function, only partial of the problem can be handled by K-means optimization. To provide an integrated solution, an auxiliary binary matrix is nontrivally introduced so that COR completely and efficiently solves the challenging problem via a unified K-means-- with theoretical supports. Extensive experimental results on numerous data sets in various domains demonstrate the effectiveness and efficiency of COR significantly over state-of-the-art methods in terms of cluster validity and outlier detection. Some key factors in COR are further analyzed for practical use. Finally, an application on flight trajectory is provided to demonstrate the effectiveness of COR in the real-world scenario.