Anomaly Detection via Mean Shift Density Enhancement

TL;DR

This paper introduces MSDE, an unsupervised anomaly detection method that leverages density-driven manifold evolution, demonstrating robustness and superior performance across diverse real-world datasets and noise conditions.

Contribution

MSDE is a novel unsupervised framework that detects anomalies based on their geometric response to density-driven manifold evolution, improving robustness over existing methods.

Findings

MSDE outperforms 13 baselines on the ADBench benchmark.

MSDE maintains strong performance across various noise levels.

Displacement-based scoring enhances anomaly detection robustness.

Abstract

Unsupervised anomaly detection stands as an important problem in machine learning, with applications in financial fraud prevention, network security and medical diagnostics. Existing unsupervised anomaly detection algorithms rarely perform well across different anomaly types, often excelling only under specific structural assumptions. This lack of robustness also becomes particularly evident under noisy settings. We propose Mean Shift Density Enhancement (MSDE), a fully unsupervised framework that detects anomalies through their geometric response to density-driven manifold evolution. MSDE is based on the principle that normal samples, being well supported by local density, remain stable under iterative density enhancement, whereas anomalous samples undergo large cumulative displacements as they are attracted toward nearby density modes. To operationalize this idea, MSDE employs a weighted mean-shift procedure with adaptive, sample-specific density weights derived from a UMAP-based fuzzy neighborhood graph. Anomaly scores are defined by the total displacement accumulated across a small number of mean-shift iterations. We evaluate MSDE on the ADBench benchmark, comprising forty six real-world tabular datasets, four realistic anomaly generation mechanisms, and six noise levels. Compared to 13 established unsupervised baselines, MSDE achieves consistently strong, balanced and robust performance for AUC-ROC, AUC-PR, and Precision@n, at several noise levels and on average over several types of anomalies. These results demonstrate that displacement-based scoring provides a robust alternative to the existing state-of-the-art for unsupervised anomaly detection.