Discriminant Analysis: Classifying Correlated Gaussian Clusters

Two multivariate-Gaussian classes float in 3D space, each with its own tunable covariance ellipsoid. This simulator computes the real Bayes discriminant function δ_k(x) = -½(x-μ_k)'Σ_k⁻¹(x-μ_k) - ½ln|Σ_k| + ln π_k for every point and renders the exact decision surface where the two classes tie — a flat plane under Linear Discriminant Analysis' shared-covariance assumption, or a curved quadric surface under Quadratic Discriminant Analysis' per-class covariance. Drag the correlation sliders to reshape each class's covariance ellipsoid, pull the means apart, resample points, and watch live classification accuracy update as misclassified points light up red.