Techniques
Methods
A Method note explains one technique: what it computes, what it discards, and when to reach for it over its nearest neighbour. Each one heads a tag — the tag page lists everything that shares it, and the Method note says why those things belong together.
- Mapper Compress a dataset into a graph by covering the range of a chosen filter function and clustering within each piece. method/mappermodality/point-cloudmodality/high-dim-tabular
- Multiparameter Persistence Filter along two parameters at once — scale and density, say — when one axis cannot separate structure from noise. method/multiparameter-persistencemethod/persistent-homologymodality/point-cloud
- Persistent Homology Track holes across every scale at once instead of picking one, and record where each appears and dies. method/persistent-homologymodality/point-cloud
- Persistent Topological Laplacians A Laplacian family built along a filtration; its zero eigenvalues are persistent homology, and the rest are the geometry persistence throws away. method/persistent-laplacianmethod/persistent-homologyapplication/molecular-sciencesmodality/point-cloudmodality/graph
- Simplicial Learning Learn on the complex itself — message passing over simplices and their Hodge structure rather than over graph edges. method/simplicial-learningmethod/topological-deep-learningmodality/graph
- Spectral Geometry Recover a dataset's latent geometry from the spectrum of an operator built on its neighbourhood graph, rather than assuming a shape in advance. method/spectral-geometryapplication/single-cellmodality/high-dim-tabularmodality/point-cloud
- Topological Deep Learning Learn the readout instead of hand-picking it — topological structure as input to a model, or as the domain the model operates on. method/topological-deep-learningmethod/persistent-homologyapplication/molecular-sciencesapplication/structure-qamodality/graph