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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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Presentation Transcript
slide1

Optimization Theory

Primal Optimization Problem

subject to:

Primal Optimal Value:

slide2

Optimization Theory

Convex Optimization Problem

subject to:

: convex functions

slide3

Optimization Theory

Primal Lagrangian function

subject to:

slide4

Optimization Theory

Kuhn-Tucker Theory

KKT Complementarity Condition

slide5

Optimization Theory

Dual Lagrangian Function

slide6

Optimization Theory

Dual Optimization problem

subject to:

subject to:

Primal

Dual

For convex optimization problem:

slide7

Support Vector Machine (SVM)

  • SVM
  • Classification
  • Regression
  • Linear SVM
  • Nonlinear SVM
slide8

Support Vector Machine (SVM)

  • Linear SVM
  • Training
  • Prediction
slide9

Support Vector Machine (SVM)

  • Linear SVM Training

Training dataset:

Optimal Separating Hyperplane:

slide10

Support Vector Machine (SVM)

  • Linear SVM Prediction

Testing dataset:

slide11

Support Vector Machine (SVM)

  • Linear SVM: Separable case
  • The optimal hyperplane is obtained by maximizing the margin
  • Support vectors
slide12

Support Vector Machine (SVM)

  • Linear SVM: Separable case

Primal Problem

slide13

Support Vector Machine (SVM)

  • Linear SVM: Separable case
slide14

Support Vector Machine (SVM)

  • Linear SVM: Separable case
slide15

Support Vector Machine (SVM)

  • Linear SVM: Separable case
slide16

Support Vector Machine (SVM)

  • Linear SVM: Separable case

Dual Problem

slide17

Support Vector Machine (SVM)

  • Linear SVM: Separable case
slide18

Support Vector Machine (SVM)

  • Linear SVM: Non-separable case
slide19

Support Vector Machine (SVM)

  • Linear SVM: Non-separable case
slide20

Support Vector Machine (SVM)

  • Linear SVM: Non-separable case
slide21

Support Vector Machine (SVM)

  • Linear SVM: Non-separable case (Primal Problem)

Subject to:

slide22

Support Vector Machine (SVM)

  • Linear SVM: Non-separable case (Primal Problem)
slide23

Support Vector Machine (SVM)

  • Linear SVM: Non-Separable case
slide24

Support Vector Machine (SVM)

  • Linear SVM: Non-separable case (Implementation)

Quadratic programming Problem

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