This article introduces the Gaussian Mixture Model as a natural extension of k-Means, by improving how distance is measured through variances and the Mahalanobis distance. Instead of assigning points to clusters with hard boundaries, GMM uses probabilities learned through the Expectation–Maximization algorithm – the general form of Lloyd’s method.
Using simple Excel formulas, we implement EM step by step in 1D and 2D, and we visualise how the Gaussian curves or ellipses move during training. The means shift, the variances adjust, and the shapes gradually settle around the true structure of the data.
GMM provides a richer, more flexible way to model clusters, and becomes intuitive once the process is made visible in a spreadsheet.
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