Quadratic Discriminant Gaussian Boundary
Derive curved Gaussian class boundaries while preserving priors and covariance normalization.
Free theory articleDerive curved Gaussian class boundaries while preserving priors and covariance normalization.
Concept & interpretation
Quadratic Discriminant Analysis (QDA) is a generative model used for classification. Unlike Linear Discriminant Analysis (LDA), which assumes all classes share the same covariance matrix, QDA estimates a separate covariance matrix for each class.
Experiment
You can test the decision boundary curvature and point evaluations in the interactive module:Quadratic Discriminant Gaussian Boundary.
- Set the Covariances control to "Equal". Observe that the boundary becomes a straight line, as the quadratic terms cancel out (coefficients become 0).
- Change the Covariances to "Different". The boundary is now curved (a hyperbola or ellipse) due to the distinct class variances.
- Set the Prior A to "0.75" and observe how the decision boundary shifts to favor Class A.
- Adjust Point x and Point y to explore different regions of the feature space and see how the posterior probabilities update.