Updates and Boundaries

Correcting a Boundary

The perceptron keeps a boundary state and changes it when a displayed row is on the wrong side or exactly on the line. This opening lesson shows only the signed training rows and their fixed order, so the later arithmetic has a visible source.

highlighted = computed this step

Signed training points

The perceptron starts with exact signed points in a fixed order. The first point is (1, 0) with label 1, and the third point is (0, 1) with label -1.

(xi,yi) are exact signed rows(x_i,y_i)\text{ are exact signed rows}
Training pointsOnly the fixed-order signed training set is shown.Training pointsPerceptron training pointsExact signed training points in fixed order.0:+11:+12:-13:-1fixed order: 0, 1, 2, 3

Why the order is fixed

Updates depend on the row order, so the renderer treats the order as part of the shown data. Here the order is 0, 1, 2, 3.

order=[0,1,2,3]\text{order}=[0,1,2,3]
Training pointsOnly the fixed-order signed training set is shown.Training pointsPerceptron training pointsExact signed training points in fixed order.0:+11:+12:-13:-1fixed order: 0, 1, 2, 3

Summary

No boundary or update has been shown yet. This lesson fixes the exact rows that every later step must reuse.

fixed signed data only\text{fixed signed data only}
Training pointsOnly the fixed-order signed training set is shown.Training pointsPerceptron training pointsExact signed training points in fixed order.0:+11:+12:-13:-1fixed order: 0, 1, 2, 3