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Optimization Theory. Primal Optimization Problem. subject to:. Primal Optimal Value:. Optimization Theory. Convex Optimization Problem. subject to:. : convex functions. Optimization Theory. Primal Lagrangian function. subject to:. Optimization Theory. Kuhn-Tucker Theory.
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Optimization Theory Primal Optimization Problem subject to: Primal Optimal Value:
Optimization Theory Convex Optimization Problem subject to: : convex functions
Optimization Theory Primal Lagrangian function subject to:
Optimization Theory Kuhn-Tucker Theory KKT Complementarity Condition
Optimization Theory Dual Lagrangian Function
Optimization Theory Dual Optimization problem subject to: subject to: Primal Dual For convex optimization problem:
Support Vector Machine (SVM) • SVM • Classification • Regression • Linear SVM • Nonlinear SVM
Support Vector Machine (SVM) • Linear SVM • Training • Prediction
Support Vector Machine (SVM) • Linear SVM Training Training dataset: Optimal Separating Hyperplane:
Support Vector Machine (SVM) • Linear SVM Prediction Testing dataset:
Support Vector Machine (SVM) • Linear SVM: Separable case • The optimal hyperplane is obtained by maximizing the margin • Support vectors
Support Vector Machine (SVM) • Linear SVM: Separable case Primal Problem
Support Vector Machine (SVM) • Linear SVM: Separable case
Support Vector Machine (SVM) • Linear SVM: Separable case
Support Vector Machine (SVM) • Linear SVM: Separable case
Support Vector Machine (SVM) • Linear SVM: Separable case Dual Problem
Support Vector Machine (SVM) • Linear SVM: Separable case
Support Vector Machine (SVM) • Linear SVM: Non-separable case
Support Vector Machine (SVM) • Linear SVM: Non-separable case
Support Vector Machine (SVM) • Linear SVM: Non-separable case
Support Vector Machine (SVM) • Linear SVM: Non-separable case (Primal Problem) Subject to:
Support Vector Machine (SVM) • Linear SVM: Non-separable case (Primal Problem)
Support Vector Machine (SVM) • Linear SVM: Non-Separable case
Support Vector Machine (SVM) • Linear SVM: Non-separable case (Implementation) Quadratic programming Problem