Support Vector Machines
Find the widest street between two classes. That is the entire idea. Language: Python Implement a linear SVM from scratch using hinge loss and gradient descent on the primal formulation. Explain the maximum margin principle and identify support vectors from a trained model. Compare linear, polynomial, and RBF kernels and explain how the kernel trick avoids explicit high-dimensional mapping. Evaluate the tradeoff controlled by the C parameter between margin width and classification errors. You have two classes of data points and need to draw a line (or hyperplane) separating them. Infinitely many lines could work. Which one should you pick? The one with the biggest margin. The margin is the distance between the decision boundary and the nearest data points on each side. A wider margin means the classifier is more confident and generalizes better to unseen data. This intuition leads to Support Vector Machines, one of the most mathematically elegant algorithms in ML. SVMs were the dominant classification method before deep learning and remain the best choice for small datasets, high-dimensional data, and problems where you need a principled, well-understood model with theoretical guarantees. SVMs connect directly to Phase 1: the optimization is convex (Lesson 18), the margin is measured with norms (Lesson 14), and the kernel trick exploits dot products to handle nonlinear boundaries without ever computing in…
Support Vector Machines: Find the widest street between two classes. That is the entire idea. Language: Python Implement a linear SVM from scratch using hinge…
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