Explore topological data analysis techniques for non-Euclidean and non-metric spaces in this 57-minute talk by Hubert Wagner. Learn about adapting existing TDA tools for these contexts, understand important caveats, and discover a recent successful application in detecting backdoor attacks on neural networks. Delve into topics such as information retrieval, Euclidean distance, editor check filtration, and theoretical justifications. Gain insights on distance measurements between points, trojan attack detection, and the use of multiple distance measures in classification. Conclude with a summary, inspiration, and a Q&A session to deepen your understanding of TDA in complex data spaces.