Easy

SVM Geometric Margin

Easy

~10 min

code completion

SVM Margin

An SVM finds the hyperplane that maximizes the margin between classes. The margin is the distance between the two support hyperplanes:

margin = \frac{2}{∥ w ∥}

where $w$ is the normal vector of the decision boundary. Maximizing the margin is equivalent to minimizing $∥ w ∥$ .

The signed distance from a point $x$ to the decision boundary $w^{⊤} x + b = 0$ is:

d = \frac{w ^{⊤} x + b}{∥ w ∥}

Positive for one class, negative for the other.

Your task:

Implement svm_margin(w) that returns the geometric margin $\frac{2}{∥ w ∥}$ given the weight vector.

Example Tests

Unit vector: margin = 2

Input: {"w":[1,0]}

Expected: 2

||w||=2: margin = 1

Input: {"w":[2,0]}

Expected: 1

3-4-5 right triangle: ||w||=5, margin=0.4

Input: {"w":[3,4]}

Expected: 0.4

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