Support Vector Machines: Maximizing Margin

This lecture delves into Support Vector Machines (SVM), a classification method that maximizes the margin between classes. The instructor explains the concept of separating hyperplanes, the importance of maximizing the margin for robust classification, and the role of support vectors in defining the hyperplane. The lecture covers the historical background of SVM, its significance before the rise of neural networks, and the introduction of convex duality. The instructor also discusses the transition from hard SVM to soft SVM for non-linearly separable data, explaining the relaxation of constraints and the trade-off between margin size and misclassification. The dual formulation of SVM is explored, highlighting the sparsity of support vectors and the significance of the kernel matrix in simplifying optimization. The lecture concludes with insights on the importance of support vectors in defining the optimal predictor and the role of SVM in learning decision boundaries.