Course 16 Geometric and Topological Data Analysis

Topological Data Analysis (TDA) is a modern approach in data science that leverages concepts from algebraic topology to study the shape and structure of data. By focusing on the connectivity and geometric features of data, TDA provides powerful tools for capturing high-dimensional patterns and relationships that might be missed by traditional statistical methods. Key techniques, such as persistent homology, allow for identifying topological features like loops and voids across multiple scales, making TDA particularly useful in fields such as image analysis, genomics, neuroscience, and complex systems modeling. Its ability to summarize complex datasets into simplified topological summaries has made it a valuable tool for theoretical exploration and practical applications in data analysis.