Discriminant Analysis 2D: LDA vs QDA on Correlated Gaussian Clusters

Two bivariate-Gaussian classes sit in the (x,y) plane, each with its own tunable covariance ellipse. 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 boundary where the two classes tie — a straight line under Linear Discriminant Analysis' shared-covariance assumption, or a curved conic under Quadratic Discriminant Analysis' per-class covariance. A synced heatmap panel shows the raw discriminant score field, and a bar panel tracks each class's live covariance eigenvalues. Drag the correlation sliders to reshape each class's covariance ellipse, pull the means apart, resample points, pan/zoom the main view, and watch live classification accuracy update as misclassified points light up red.