BIZNIQUE / LINEAR ALGEBRA / 31
Measure perpendicular distance to a boundary
Measure perpendicular distance to a boundary
Move a line and distinguish perpendicular distance from a horizontal or vertical gap.
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THE IDEA
Read the example.
Read the example.
A line in two dimensions and a plane in three dimensions are examples of a hyperplane. The nearest point is reached along the normal direction. The formula requires w to be nonzero.
d = |wᵀx + b| / ‖w‖₂
Use it well
Use it well
The signed expression tells you which side of the boundary contains the point. The absolute value gives distance and discards that side information.
TRY IT YOURSELF
A quick check.
A quick check.
For x = (3, 4) and the line x₁ = 1, what is the perpendicular distance?
Check your reasoning
Check your reasoning
Use w = (1, 0), b = −1. The distance is |3−1| = 2.
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