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This lecture covers the concepts of clustering and density estimation. It starts with a recap of Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA). Then, it delves into the basics of clustering using K-means algorithm, explaining the properties, algorithm, and the elbow method. The lecture also introduces Gaussian Mixture Models (GMM) and Kernel Density Estimation (KDE) as non-parametric density estimation methods. It concludes with Mean Shift algorithm for clustering by finding density maxima. The exercises focus on Gaussian mixture models and kernel density estimation.