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.

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.

Support Vector Machine Margin

Hard/soft-margin SVM sketch with C penalty, hinge loss, support vectors, decision boundary, and margin bands.

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

About this model

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

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.

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Support Vector Machine Margin

Live graphs

About this model

How it works

Key equations

Frequently asked questions

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Live graphs

About this model

How it works

Key equations

Frequently asked questions