The field of machine learning and data analysis is moving towards a greater emphasis on understanding the geometric and topological structure of data. Recent research has highlighted the importance of considering the geometry of data in metric spaces, and has proposed new methods for analyzing and enhancing the quality of training data. The use of persistent homology and other topological techniques has been shown to be effective in denoising recurrent signals, tracking the evolution of topological features, and understanding the geometry of text embeddings. Furthermore, the development of new metrics and methods for evaluating the reliability of datasets has the potential to improve the robustness and accuracy of machine learning models. Notable papers in this area include: Predict Training Data Quality via Its Geometry in Metric Space, which proposes a new method for analyzing the geometry of training data using persistent homology. Region-Aware Wasserstein Distances of Persistence Diagrams and Merge Trees, which introduces a new metric for comparing topological features in data. When Annotators Disagree, Topology Explains, which demonstrates the use of topological data analysis in understanding the geometry of text embeddings and resolving ambiguity in natural language processing tasks.