This animation visualizes how raw classifier scores are turned into predictions, contrasts one-versus-rest and one-versus-one multiclass strategies, and shows a perceptron updating weights for true versus predicted classes. It then focuses on the XOR problem, showing no line separates the classes in the original plane, but adding the feature x1*x2 makes the decision rule linear in the new space. Useful for first-year AI students learning why feature transformations enable linear classifiers to solve nonlinear problems.
Narrated · 16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
# Nonlinear boundaries can be linear in a new representation Begin with three class scores [1.2,-0.4,0.9] and select the largest, making clear that raw scores are not probabilities. Compare one-versus-rest and one-versus-one classification: four classes require four or six binary models respectively. Briefly show a multiclass perceptron updating the true and predicted class weights in opposite directions. Then focus on XOR: label (0,0) and (1,1) negative, and (1,0) and (0,1) positive. No straight line separates these labels in the original plane. Add the feature x1*x2 and evaluate g(x) = x1 + x2 - 2*x1*x2 - 0.5. The four scores are negative for the diagonal pair and positive for the other pair. Explain that this decision rule is linear in the expanded features but nonlinear in the original coordinates. Use black backgrounds, clear axis labels, and cyan and orange classes. Audience: 一年级人工智能专业学生