Support Vector Classifier, Explained: A Visual Guide with Mini 2D Dataset

Support Vector Machines (SVMs) are supervised learning models primarily used for classification tasks. They aim to find the line that best divides a dataset into classes, maximizing the margin between these classes. The primal form of SVM seeks to find a hyperplane that correctly classifies all data points and maximizes the distance between this hyperplane and the nearest data points from each class. In the case of soft margin SVM, the primal form allows for some misclassification and uses slack variables to quantify the degree of misclassification or margin violation. The dual form provides an alternative way to solve the SVM optimization problem, leading to computational advantages. It uses Lagrange multipliers, which show the relationship between data points and the decision boundary. Sequential Minimal Optimization (SMO) is an algorithm used to solve for the optimal Lagrange multipliers. After solving the SVM optimization problem, the decision function can be used to classify new data points.