Detecção automática de Aanomalias baseada em Difusão Geométrica Markoviana

Abstract

Automatic anomaly detection is essential in domains such as healthcare, finance, and cybersecurity, where small deviations may indicate fraud, failure, or imminent risk. This study introduces an unsupervised method called Anomaly Detection based on Marko- vian Geometric Diffusion (DA-DGM), applicable to one-dimensional and multi-dimensional datasets. The technique employs geometric diffusion to identify nonlinear relationships among instances; in multi-dimensional data, the scale parameter is tuned via Shannon entropy using a global search followed by local refinement, ensuring adaptability to the data context. The main contribution lies in integrating the sensitivity of Markovian geometric diffusion with automatic scale-parameter tuning based on Shannon entropy, thereby eliminating reliance on manual hyperparameter adjustment and providing a di- rectly interpretable anomaly metric grounded in self-transition probability. In evaluations on synthetic and real datasets, DA-DGM matches or surpasses classical methods such as KNN (k-Nearest Neighbors) and LOF (Local Outlier Factor), and achieves competitive performance against IForest (Isolation Forest) in terms of area under the ROC curve (AUC-ROC), with particular advantages in scenarios of complex geometry and low ano- maly prevalence. These results highlight DA-DGM’s potential for critical applications and reinforce the usefulness of diffusion-based approaches in data mining.