A LINEAR CLASSIFIER

The perceptron

Can a straight line separate your points? Build a dataset, then teach a classifier one example at a time.

Add a point with the keyboard

This step, worked out

Press Step one point to begin.

Calculations use the weights before this step. The plot and model values show the result after this step. Displayed decimals are rounded.

1. Choose your data

The simple example has three numbered points and starts with η = 1. Use Step one point to work through it, or Run for a slow walkthrough. XOR cannot be separated by a single straight line. Try it and see why training keeps going.

2. Train the model

Learning rate η 1

Pass0

Updates0

Correct*—

*Positive signed margin: y(w · x + b) > 0. Points exactly on the line trigger an update.

Move the boundary yourself

Change the weights to turn the line; change b to slide it. Training continues from your chosen values. Adjusting a control pauses training and restarts the pass count.

w₁ 0 w₂ 0 b 0

The green arrow shows the direction of w toward increasing scores. Its display length is fixed; it does not show ‖w‖.

Inside the model

Score = w₁x₁ + w₂x₂ + b. Blue shading means a positive score; orange means negative. The line has score zero.

If y(w · x + b) ≤ 0:
w ← w + ηyx
b ← b + ηy

Press Step to inspect the first example.