用异常检测反推聚类,少标注也能精准分组。
Seed-Guided Semi-Supervised Clustering by A-Contrario Anomaly Detection

- 把聚类看作异常检测的反问题,通过统计推理找无异常点集。
- 10~30个种子标签即可达到强性能,线性扩展适合大规模数据。
- 无需调参,自动识别噪声和未知簇,适合小样本场景。
本文提出一种基于统计对偶性的半监督聚类框架,解决噪声环境下鲁棒聚类定义难题。传统划分算法易误将离群点归入簇中,而密度方法对全局参数敏感。基于a-contrario统计推理与格式塔邻近原则,将簇定义为相对于均匀随机假设无异常点的最大子集。核心是感知算法(Perception),采用期望值阈值(𝔼 < 1)自动识别离群点,无需人工调参。通过迭代“排除式聚类”机制,利用少量用户标注的种子初始化簇中心,逐步吸纳非异常点扩展簇结构。该方法自然分离边缘点、孤立噪声及新出现的未知簇。在合成数据及图像、文本等真实数据集上评估,使用每簇10~30个种子标签,在低调参基准下表现优异,且对样本量和维度保持线性可扩展性。
原文摘要 · Abstract (English)
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 \textit{a-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 ($\mathbb{E} < 1$) 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.
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