Multiclass Classification: One-vs-Rest vs One-vs-One

Binary classifiers only draw one line between two classes, so real multiclass problems need a decomposition strategy on top. This simulator trains real logistic-regression classifiers with batch gradient descent on a synthetic 2D dataset and renders the resulting decision surface as a live 3D landscape: cell color shows the predicted class and cell height shows how confident that prediction is. Switch between One-vs-Rest (one classifier per class, argmax wins) and One-vs-One (one classifier per class pair, majority vote wins) on the same data to see how the boundaries — and the number of classifiers trained — genuinely differ, then change the class count, cluster spread, or resample the dataset to retrain everything from scratch.