Anomaly Detection Based on Markovian Geometric Diffusion

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.