Topological data analysis for neuroscience

Topological Data Analysis (TDA) to examine topological features of point clouds.

Topological data analysis (TDA) is an approach that uses algebraic topology to analyze complex data sets, including point clouds. With TDA, the user can evaluate the degree of noise, variability, and complexity, as well as identifying topological features such as holes, loops, and voids in the point clouds at different scales. This approach is based on tools like vietoris-rips complexes and persistent homology that allow to visualize complex topological structures.

Example of Vietoris-Rips complexes.

A first approach is available in this prepint and its corresponding repository. If you have any ideas or want to implement this approach to your research, please feel free to contact me. I also recommend to get in touch with my colleague Dhananjay Bhaskar for this matter.