Speaker
Description
Modern machine learning often relies on finding useful representations of complex, structured data. For data with an underlying geometric structure such as point clouds, images, graphs, or time series, TDA provides tools for constructing representations that capture shape across multiple scales. In this minicourse, I will recall the intuitions of TDA, and introduce the associated statistical and machine learning framework. Then, I'll illustrate how topological features can be extracted from data and how the resulting descriptors can be integrated into typical machine learning pipelines. This includes unsupervised learning (vectorization), kernels (e.g., Sliced Wasserstein), and modern machine learning integration (e.g., autodiff handling).
Finally, I'll generalize these constructions to the multiparameter persistence setting.