This lecture covers the clustering problem, where points are grouped into clusters based on distance measures in high-dimensional space. It discusses the characteristics, methods, and examples of clustering, including hierarchical clustering and K-means. The instructor explains the challenges of clustering in high-dimensional spaces and provides insights into the K-means algorithm, its properties, drawbacks, and ways to determine the optimal number of clusters. Additionally, density-based clustering methods like DBSCAN are introduced, highlighting their advantages over centroid-based methods. The lecture concludes with a detailed explanation of DBSCAN algorithm and its performance.