# Seed-Guided Semi-Supervised Clustering by A-Contrario Anomaly Detection

arXiv: https://arxiv.org/abs/2606.18833 · HTML: https://mlsanity.com/paper/2606.18833/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 37 references that are in the map.
- First posted on arXiv 17 Jun 2026.

## Builds on (most cited first, 9 of 9)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [Towards K-means-friendly Spaces: Simultaneous Deep Learning and Clustering](https://mlsanity.com/paper/1610.04794/) (2016)
- [Deep Clustering: A Comprehensive Survey](https://mlsanity.com/paper/2210.04142/) (2022)
- [Clustering with Outlier Removal](https://mlsanity.com/paper/1801.01899/) (2018)
- [Semi-Supervised Constrained Clustering: An In-Depth Overview, Ranked Taxonomy and Future Research Directions](https://mlsanity.com/paper/2303.00522/) (2023)
- [Anomaly Detection using Principles of Human Perception](https://mlsanity.com/paper/2103.12323/) (2021)
- [Extension of the Dip-test Repertoire -- Efficient and Differentiable p-value Calculation for Clustering](https://mlsanity.com/paper/2312.12050/) (2023)
- [Hierarchical Reference Sets for Robust Unsupervised Detection of Scattered and Clustered Outliers](https://mlsanity.com/paper/2603.12847/) (2026)

## Abstract (arXiv)

This paper introduces a semi-supervised clustering framework grounded in the statistical duality between grouping principles and anomaly detection. We address the challenge of robust cluster definition in noisy environments -- a task where partitioning algorithms often over-assign outliers and density-based methods remain sensitive to heuristic global parameters. Drawing on textita-contrario statistical reasoning and Gestalt proximity principles, we define a cluster as a maximal subset of data points containing no anomalies relative to a null hypothesis of uniform randomness. Central to this approach is the Perception algorithm, which utilises a principled expectation-based threshold (mathbbE < 1) to identify outliers without manual parameter tuning. By treating clustering as the dual of anomaly detection, we employ an iterative ``clustering-by-exclusion'' mechanism. The algorithm is seed-guided, leveraging minimal user-provided labels to initialise robust cluster medians and form initial groups, which are subsequently expanded by admitting non-anomalous points. This approach naturally isolates fringe points, isolated noise, and emerging unknown clusters. We evaluate the method on synthetic and real-world benchmarks, including image and text datasets represented through raw, linear-reduced, and neighbourhood-preserving embeddings. Results demonstrate that with as few as 10--30 seeds per cluster, the proposed method achieves competitive and often very strong performance under a practical low-tuning benchmarking protocol, while maintaining linear scalability with respect to both observations and dimensionality for a fixed number of seeded clusters and iterations.