Demo 1: Explicit feature map φ(x) into 3D to reveal linear separability
Left: click to add 1D labeled points. Right: view the lifted points in 3D feature space:
(x, φ₂(x), φ₃(x)). Choose φ₂, φ₃ as expressions in x (you can use sin, cos, exp, abs, etc.).
Click “Fit linear separator” to run a perceptron in feature space and draw a separating plane (if separable).
class +1
class −1
Tip: The example is “outer points are +1, inner points are −1”, which is not separable by a 1D threshold.
Try φ₂(x)=x^2 and φ₃(x)=x (or x^3), then fit a plane.