Perceptron
One neuron, one boundary
A single weighted sum plus threshold showed that machines could learn a classifier directly from data.
Perceptron Demo
Click in the chart to drop a point of the selected class. Then run the perceptron — each pass updates the weights only for the points it gets wrong. The line below is w · x + b = 0.
click chart to add a + point · misclassified points have a yellow ring
1.00·x₁ − 1.00·x₂ + 0.50 = 0
The update rule
For each misclassified point, push the weight vector in the direction of its true class:w ← w + η · y · x, b ← b + η · y. Correctly classified points are skipped — they pull no force.
Why it converges
If the classes are linearly separable, the perceptron is guaranteed to find a separating hyperplane in finite steps (Novikoff, 1962). Try a non-separable cloud — it will oscillate without settling.