This paper investigates the integration of Topological Data Analysis (TDA) with game-theoretic frameworks to address vulnerability to data poisoning in machine learning systems. We establish novel metrics for quantifying the susceptibility of data structures to adversarial manipulation through their topological characteristics. Our research demonstrates that topological features derived from persistence diagrams provide effective indicators for detecting poisoning attempts and designing defensive strategies. By framing the adversarial interaction as a Nash equilibrium problem, we develop robust countermeasures with theoretical guarantees. Experimental validation confirms the effectiveness of our approach across multiple datasets and attack scenarios.
Keywords: Topological Data Analysis, Game Theory, Data Poisoning, Adversarial Machine Learning, Persistent Homology.
Citation: M. Ferrara., (2025). Integrating Topological Data Analysis and Game Theory for Robust Machine Learning. J AI & Mach Lear., 1(1):1-3.