Q8: What is a margin in SVM?

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In Support Vector Machines (SVM), the margin is the distance between the decision boundary (the separating hyperplane) and the closest data points from each class.

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📌 Key Points:

1. Support Vectors

   • The data points that lie closest to the decision boundary.

   • They "support" or define the position and orientation of the boundary.

2. Margin Definition

   • The margin is measured as the perpendicular distance from the decision boundary to the nearest support vector from either class.

   • In a maximum-margin classifier, SVM chooses the boundary that maximizes this distance.

3. Why Maximize the Margin?

   • A larger margin means the decision boundary is farther from any training data point, which usually improves generalization on unseen data.

   • This aligns with the structural risk minimization principle: simpler decision boundaries generalize better.

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📐 Formula for Margin

For a linear SVM, the margin $M$ is:

$$M = \frac{2}{\|w\|}$$

Where:

• $w$ = weight vector defining the hyperplane $w \cdot x + b = 0$

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🖼 Intuition Example:

Imagine two parallel lines enclosing the training points of both classes:

• The middle line between them is the decision boundary.

• The distance from this middle line to either parallel line is half the margin.

• SVM’s goal is to push these lines as far apart as possible while still separating the classes.

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If you want, I can create a visual diagram showing an SVM decision boundary with the margin and support vectors labeled. That usually makes this concept much clearer.
Do you want me to make it?

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