Practical Clustering and Topological Data Analysis

Explore the evolution of clustering techniques in data science through a topological lens in this comprehensive lecture. Delve into a historically-grounded overview of clustering methods, from non-topological algorithms like k-means to advanced topological approaches such as single linkage clustering. Examine modern techniques including DBSCAN and HDBSCAN, and understand the role of dimensionality reduction methods like UMAP in clustering problems. Gain insights into practical applications of these algorithms in real-world scenarios, supported by relevant citations and theoretical foundations. This talk, part of the "Topological Data Analysis - Theory and Applications" workshop, offers a unique perspective on the intersection of topology and data science, providing valuable knowledge for both practitioners and researchers in the field.