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Intuition behind maximizing the geometric margin in SVM:
- Confidence in Prediction: Points far away from the decision boundary (hyperplane) are classified with higher confidence. Maximizing the margin ensures that the training examples, especially the support vectors, are as far as possible from the boundary, leading to high confidence in their classification
- Improved Generalization: A larger margin generally leads to a classifier that generalizes better to unseen data. It creates a wider “street” or “gap” between the classes, making the model less sensitive to minor variations or noise in new data points
- Regularization: Maximizing the margin acts as a form of regularization. It penalizes overly complex models and helps prevent overfitting by finding the simplest decision boundary that separates the classes with the largest possible gap