Discover the shape of data using algebraic topology through 26 interactive demonstrations.
See also: Algebraic Topology for the homology theory persistent homology builds on, Topology for the simplicial complexes that turn point clouds into shapes, and Machine Learning for the manifold hypothesis that motivates topological feature extraction.
Build the foundations of TDA: understand point clouds as data representations and simplicial complexes as the building blocks for topological analysis.
Learn to construct simplicial complexes from point cloud data using the Vietoris-Rips and Čech constructions.
Discover how homology groups count topological features: connected components (H₀), loops (H₁), and voids (H₂).
Track the birth and death of topological features across scales. Learn the matrix reduction algorithm at the heart of TDA.
Master the visual representations of persistence: barcodes, persistence diagrams, and how to interpret them.
See TDA solving real problems: protein structure analysis, single-cell genomics, time series, and network analysis.