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This article explains how hard‑margin and soft‑margin support vector machines handle perfectly and approximately linearly separable data, introduces slack variables and penalty parameters, derives the quadratic programming and dual formulations, and shows how the resulting classifier works on unseen samples.
Support Vector Machines (SVM), introduced in 1992, are powerful data‑mining methods based on statistical learning theory that excel at handling small‑sample, nonlinear, and high‑dimensional regression and classification tasks, with distinct formulations for classification (SVC) and regression (SVR).
This article explains the fundamentals of Support Vector Machines, describes how they separate data with optimal hyperplanes, provides a 2‑D example with visualizations, and includes Python code using scikit‑learn to generate synthetic data, plot points, and illustrate possible decision boundaries.
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