December 4, 2025Open Access

Anomaly Detection Based on Markovian Geometric Diffusion

ERErikson Carlos Ramos LSLeandro Carlos De Souza GMGustavo Henrique Matos Bezerra Motta

Key Points

Anomaly detection enhances identification of subtle deviations in critical applications such as finance and healthcare.
The scale parameter tuning currently employs Shannon entropy and promotes adaptability with global and local refinement.
Evaluation shows significant performance improvements over classical methods like KNN and IForest in processing multidimensional datasets.
This technique highlights important advancements in data mining, particularly with heterogeneous datasets.

Abstract

Automatic anomaly detection is vital in domains such as healthcare, finance, and cybersecurity, where subtle deviations may signal fraud, failures, or impending risks. This paper proposes an unsupervised anomaly-detection method called Anomaly Detection Based on Markovian Geometric Diffusion (AD-MGD). The technique is applicable to uni- and multidimensional datasets, employing Markovian Geometric Diffusion to uncover nonlinear structures in the relationships among instances. For multidimensional data, the scale parameter, which is crucial to the performance of the method, is tuned using Shannon entropy. The approach includes a global search followed by local refinement of the scale parameter, promoting adaptability to the data context. Experimental evaluations on synthetic and real datasets show that AD-MGD consistently outperforms classical methods such as KNN, LOF, and IForest in terms of area under the ROC curve (AUC), particularly in heterogeneous data scenarios. The results highlight the potential of AD-MGD in critical anomaly-detection applications, advancing the use of diffusion techniques in data mining.

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