Gaussian Mixture Models: Soft Clustering with Expectation-Maximization

Most introductions to unsupervised learning stop at k-means, where every point is forced into exactly one cluster. This simulator instead runs real Expectation-Maximization on a Gaussian Mixture Model: each of the K components owns a full 2D covariance ellipse, not just a centroid, and every data point carries a soft probability of belonging to each one — visualised as a colour blend rather than a hard label. A live 3D density surface rises and reshapes above the data plane after every M-step, tracing the actual mixture probability density the model believes in, while the log-likelihood, its step-to-step change, and the mean responsibility entropy are read out numerically so you can watch the algorithm provably climb toward a local optimum and settle.