Why does SVM use margin maximization?

When the training data are linearly separable, there are infinite separation hyperplanes, which can correctly separate the two kinds of data. The perceptron uses the misclassification minimization strategy to obtain the separation hyperplane, but there are infinite solutions at this time. Linear separable support vector machine uses margin maximization to obtain the optimal separation hyperplane. At this time, the solution is unique. On the other hand, the classification result generated by the separated hyperplane is the most robust and has the strongest generalization ability for unknown instances. We can take this opportunity to explain the relationship between geometric margin and functional margin.

Margin Maximization

A model with the smallest C has the widest margin, and a model with the largest C has the narrowest margin. If three SVMs have wide, medium, and narrow margins in that order, which C sequence matches them?

The shortest distance from the separating hyperplane to the nearest test observation.

University of Michigan - Ann Arbor

Maximal margin hyperplanes (AKA optimal separating hyperplanes) are used in order to find which hyperplane would give the greatest separation between output classes. These hyperplanes are found by computing the classifier margin.

SVM Maximal Margin Hyperplanes

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, pp. 3-7). New York: springer.

An Introduction to Statistical Learning with Applications in R

SVM Margin

The maximum distance from the decision boundary area to the nearest test observation.

SVM Classifier Margin

The hyperplane used to classify data depending on which side observations fall under the maximum margin hyperplane.

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