The Machine Learning “Advent Calendar” Day 5: GMM in Excel

Gaussian Mixture Models (GMM) are an extension of k-Means clustering that incorporates variance, effectively representing data as a mixture of several Gaussian distributions. The model is trained using the Expectation-Maximization (EM) algorithm, which is a more generalized version of the Lloyd's algorithm used in k-Means. The process involves an Expectation step to compute the probability of each point belonging to a cluster and a Maximization step to update the model's parameters like means and variances. Unlike the hard boundaries produced by k-Means, GMM provides probabilistic assignments, offering a more flexible method for defining cluster shapes. The concepts are demonstrated through a step-by-step implementation in Excel for both 1D and 2D data.