1. Machine Learning
Week 3

2. Support Vector Machine
Maximizing the margin
The Solution
Nonlinear Transforms

3. Better linear Separation
Linearly separable data
Different separating lines

4. From Intuition… Why is bigger margin better?
Which w maximizes the margin?

5. Finding w with large margin
Why is bigger margin better?
Which w maximizes the margin?

6. Linear SVM Mathematically
Goal: 1) Correctly classify all training data
if yi = +1
if yi = -1
for all i
2) Maximize the Margin
What we know:
w . x+ + b = +1
w . x- + b = -1
w . (x+-x-) = 2
Maximize
Minimize

7. Linear SVM Mathematically
minimize
Constrained optimization problem !
Subject to
Integrating the constraints into the Lagrangian form, we get:
Mimize J with respect to w and b, and maximize with respect to α

8. Dual Form

9. Let’s find hyperplane (example)

10. Let’s find hyperplane (example)

11. Let’s find hyperplane (example)

12. Let’s find hyperplane (example)

13. Let’s find hyperplane (example)

14. Let’s find hyperplane (example)

15. Let’s find hyperplane (example)

16. Let’s find hyperplane (example)