Machine Learning Algorithms in Depth MEAP V04 by copyright-2023-manning-publications.html

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Equation 5.9 Quadratic Primal Optimization Program for SVM

Notice, how we are essentially minimizing the regularized loss function by choosing θ with small l2 norm subject to the constraints that every training examples is correctly classified.

Figure 5.7 Max Margin Solution of SVM Classifier

Notice, as we minimize ||θ||2, we are effectively increasing the distance γi ∝ 1/||θ|| between the decision boundary and the training data points indexed by i. Geometrically, we are pushing the margin boundaries away from each other as shown in Figure 5.7. At some point, they cannot be pushed further without violating classification constraints. At this point, the margin boundaries lock into unique maximum margin solution. The training data points that lie on the margin boundaries become support vectors. Notice that we only need a subset of training examples (support vectors) to fully learn SVM model parameters.

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