The Decision Threshold - Logistic Scoring

The threshold uses the sign of the exact score. The boundary is where the score is zero, and the diagram shows that point directly.

highlighted = computed this step

The threshold rule

Class 1 is chosen exactly when z is at least 0; otherwise class 0 is chosen.

z\ge{}0\Rightarrow1

The boundary is the point where z=0. Which side a point is on is determined by the sign of z.

z=0\text{ is the boundary}

The decisions 0, 0, 1, and 1 match the shown labels. No sigmoid value was needed for this exact decision.

\text{sign}(z)\text{ decides the class}