Clustering & Density Estimation

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.

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In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is its standard deviation. The variance of the distribution is . A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate.

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