Persistent Homology

Persistent homology, a branch of topological data analysis, aims to extract meaningful shape information from complex datasets by identifying persistent topological features like connected components, loops, and voids across multiple scales. Current research focuses on integrating persistent homology with machine learning models, particularly neural networks and graph neural networks, to improve classification accuracy and interpretability in diverse applications such as image analysis, molecular property prediction, and brain connectome analysis. This approach offers a powerful way to capture higher-order relationships and global structure in data, leading to improved performance and enhanced understanding in various scientific and engineering domains.