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This lecture covers the formulation of Support Vector Machines (SVM) with hard margin, including the primal and dual formulations. It explains the interpretation of SVM parameters, the geometric interpretation of the margin, and the concept of support vectors. The lecture also discusses the dual formulation of SVM, the Lagrange multipliers, and the decision function. Additionally, it explores the algorithmic complexity of SVM in both primal and dual forms, highlighting the implications of data dimensionality on the choice between the primal and dual formulations.