Persistent Adversarial Topology: Robust TDA under Data Poisoning Attacks

Aljanabi (2023) identifies a glaring gap in defending against data poisoning in the context of federated learning, but the question remains unexplored for TDA. This research would systematically analyze how adversarial noise—whether random or targeted—modifies persistence diagrams, landscapes, and related topological summaries. The goal is to design new TDA features and filtration processes that are provably robust (or at least resilient) to such attacks. This could involve adversarial training of persistence-based features or developing “denoising” persistent homology techniques. The impact is twofold: it strengthens TDA-based anomaly detection pipelines in adversarial environments, and it grounds future theoretical work in the stability and reliability of TDA under malicious data manipulations.

References:

1. Navigating the Void: Uncovering Research Gaps in the Detection of Data Poisoning Attacks in Federated Learning-Based Big Data Processing: A Systematic Literature Review. Mohammad Aljanabi (2023). Mesopotamian Journal of Big Data.