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MNN-Closure Meets Local Maxima: A Double-Knee Approach to Anomaly Detection

MCML Authors

Walid Durani

→ Group Thomas Seidl
Database Systems, Data Mining and AI

Philipp Jahn

→ Group Thomas Seidl
Database Systems, Data Mining and AI

Thomas Seidl

Prof. Dr.

Director

Database Systems, Data Mining and AI

Abstract

Real-world datasets commonly arise from mixtures of multiple, potentially overlapping subdistributions. Traditional anomaly detection methods often use rigid assumptions or global thresholds and, as a result, struggle to identify anomalies within complex multimodal data. We propose ADM-Anomalies Detection through Local Maxima and Mutual Nearest Neighbors-an unsupervised approach that systematically identifies dense, mode-like structures without imposing a single global model. Specifically, ADM constructs a mutual nearest neighbor (MNN) graph and takes its transitive closure to reveal groups of high-density points, which converge to the true modes under mild assumptions. A “double-knee” procedure then refines these groups: (i) it separates large, high-density modes from small, fringe-like clusters, and (ii) within each major mode, it pinpoints local maxima to accommodate internal multimodality. Finally, ADM assigns an anomaly score to every point by calculating its distance to the closest local maxima, thereby identifying both globally isolated anomalies and subtle boundary anomalies. Extensive evaluations on diverse real-world datasets show that ADM consistently outperforms or matches leading baselines, all while requiring only a single hyperparameter k.

inproceedings DJS+25