There are too many resources out there on TDA, and people often say they're overwhelmed and don't know how to get started. This list is aimed at people who have not taken algebra, topology, or algebraic topology — because I haven't either. It focuses on the computation of persistent homology for point cloud data, but there's lots of other cool and relevant TDA topics like sub/super-level set filtrations, cubical homology, and so forth. Feel free to spread this around.
Recommended resources
- Connecting the Dots: Discovering the Shape of Data — TDA for kids, but a great place to start for anyone. A totally nontechnical introduction.
- Topological data analysis: One applied mathematician's heartwarming story of struggle, triumph, and ultimately, more struggle — A totally nontechnical expository article about TDA.
- Topological data analysis of collective motion — An expository article, slightly more technical.
- Topological data analysis of biological aggregation models — Uses persistent homology as a tool for exploratory data analysis.
- Self-help homology tutorial for the simple(x)-minded — Tutorial notes showing how the computation of homology of simplicial complexes is really just a linear algebra problem. This is the version without solutions to exercises; a version with solutions is also available.
- A roadmap for the computation of persistent homology — A review paper that gives a great bird's-eye look at computational tools.
- Topological Data Analysis — Another useful review paper.
- The shape of things to come: Topological data analysis and biology, from molecules to organisms — A review paper on the uses of TDA in biology.
- A topological approach to selecting models of biological experiments — Uses topological signatures to decide which of two models is a better fit for experimental data.
- Analyzing collective motion with machine learning and topology — Applying machine learning to topological signatures of data from simulations to estimate parameters.
- Introduction to the R Package TDA — A tutorial to work through.
- R-TDA package tutorial — Another tutorial to reinforce the above.