Multiparameter Persistence for Machine Learning in Topological Data Analysis

Learn about the advanced applications of Multiparameter Persistent Homology in machine learning through this technical talk that explores how multiple filtration parameters can be simultaneously utilized in Topological Data Analysis. Discover recent developments that make multiparameter persistence more practical for machine learning applications, including the introduction of novel descriptors like MMA decomposition and signed barcode. Explore how one-dimensional slices can be combined to form interval decomposable modules, and understand the vectorization and differentiability properties of these descriptors. Gain insights into how this approach extends beyond traditional single-parameter persistent homology by incorporating multiple filters such as geometrical scales, dataset sampling density, and other intrinsic data properties.