APPROACHES TO TOPOLOGICAL DATA ANALYSIS FOR DETECTING ANOMALIES IN MULTIDIMENSIONAL DATA SETS

Abstract

Abstract. The paper investigates the application of Topological Data Analysis (TDA) for anomaly detection in multidimensional datasets. The rapid growth of data volumes in modern systems – including IoT, financial monitoring, cybersecurity, and medical diagnostics – necessitates the development of robust methods capable of detecting structural anomalies in high-dimensional spaces. Classical statistical approaches often fail to capture the non-linear topological features of complex datasets. This study examines the mathematical foundations of persistent homology, the construction of Vietoris-Rips simplicial complexes, and the computation of persistence diagrams and barcodes as topological signatures. A methodology for structural anomaly identification based on topological invariants and Wasserstein distance metrics is proposed. Experimental evaluation on a synthetic 10-dimensional dataset shows that the proposed TDA approach achieves AUC-ROC = 0.951 and Precision = 0.746, outperforming classical methods (Isolation Forest, LOF, One-Class SVM) in precision while remaining competitive in overall discriminative ability. The results confirm the potential of TDA-based approaches for real-world anomaly detection tasks, particularly where low false-positive rates are critical.