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This lecture covers the theory and practice of clustering algorithms, starting with a recap of Principal Component Analysis (PCA) and introducing K-means clustering. It then delves into the concept of Fisher Linear Discriminant Analysis, spectral clustering, and the application of clustering for dimensionality reduction. The lecture also explores the graph-based connectivity approach of spectral clustering and the normalized cut method. Practical examples and demonstrations of K-means clustering and DBSCAN are provided to illustrate the concepts discussed.