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This lecture covers the Kernel K-Means algorithm, an iterative procedure involving cluster initialization, data point assignment, and centroid updating until stability. The proof of convergence is detailed, showing how the cost function changes with respect to the centroids. The influence of the RBF kernel on clustering is discussed, emphasizing the weight given to points close to clusters. The lecture also explores the interpretation of the solution in terms of density and number of points, highlighting the impact of different kernels and parameters on the clustering outcome.