Anomaly detection in financial transactions based on persistent homology
- 1,2,3,4,5 Financial University under the Government of the Russian Federation (Moscow, Russia)
Abstract
Problem statement. Anomaly detection in multidimensional financial data is an important task for financial monitoring systems and fraud detection. Classical approaches such as Local Outlier Factor and Isolation Forest, based on distance calculation or random partitioning, do not always allow identifying complex structural anomalies associated with topological features of data distribution.
Goal. To improve the efficiency of detecting anomalous financial transactions by applying the apparatus of persistent homology of topological data analysis (TDA), which analyzes the presence of one-dimensional cycles ("holes") in point distribution.
Results. A reference persistence diagram H1 was constructed for a set of normal transactions. The abnormality of a test transaction is estimated by the Wasserstein distance between the reference diagram and the diagram obtained after adding this transaction. Experiments on the publicly available PaySim dataset showed that the proposed method achieves a ROC-AUC of 0.6776, which significantly outperforms Isolation Forest (0.4068) and LOF (0.3965). The method is robust to class imbalance and does not require training on anomalies.
Practical significance. The obtained results can be used in financial monitoring tasks for detecting fraudulent transactions, as well as in other areas requiring anomaly detection in multidimensional data without training examples of anomalous behavior.
- Received
- 11.09.2026
- Approved after review
- 22.09.2026
- Accepted
- 01.10.2026
How to cite
Окунева Э.А., Белов E.Ю., Воробьев Я.И., Салихов Р.А., Рябов П.Е. Обнаружение аномалий в финансовых транзакциях на основе персистентной гомологии // Динамика сложных систем - XXI век. 2026. Т. 20. № 5. С. 105−111. DOI: https://doi.org/10.18127/j19997493-202605-14
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