Topological data analysis (TDA): study shape of data. Simplicial complex: vertices, edges, triangles, tetrahedra. Čech complex, Vietoris-Rips complex. Persistent homology: track connected components (H0), loops (H1), voids (H2) across filtration parameter ε. Barcode diagram, persistence diagram. Bottleneck distance, Wasserstein distance. Mapper: graph-based visualization of high-dimensional data — cover, cluster, nerve. Gudhi, Ripser, scikit-tda libraries. Applications: shape recognition,...
- topology
- data-science
- mathematics