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Home/Math Visualization/Support Vector Machine Margin

Support Vector Machine Margin

A support vector machine chooses a separating boundary with a large margin while penalizing violations through hinge loss. This interactive sketch lets you move the boundary, adjust the soft-margin C parameter, and see which points become support vectors because they lie on or inside the margin.

Who it's for: Machine learning, classification, optimization, statistical learning theory, and data science courses.

Key terms

  • Support vector machine
  • Margin
  • Hinge loss
  • Support vector
  • Soft margin
  • Kernel trick

This is an interactive margin sketch rather than a full quadratic-program solver; move the separator to see support vectors and hinge penalties.

Live graphs

SVM separator

62°
0
1.2
0

Measured values

Support vectors54
Mean hinge loss0.370
Accuracy100.0%

How it works

Support vector machine margin visualizer with soft-margin hinge loss, support vectors, and C parameter.

Key equations

min 1/2||w||² + C Σ max(0, 1 − y_i(w·x_i+b))
Support vectors lie on or inside the margin y(w·x+b) ≤ 1

Frequently asked questions

What makes a point a support vector?
Support vectors are the points that touch or violate the margin. They determine the fitted boundary in the optimal SVM solution.
What does C control?
C controls the penalty for margin violations. Larger C tries harder to classify training points correctly; smaller C allows more slack for a wider, more regularized margin.