Support Vector Machines - The Auton Lab

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R ∑ α An Equivalent QP 1 − R R ∑∑ k k = 1 2 k = 1 l= 1 α α Q Maximize where Q = y y x . x ) k l Copyright © 2001, 2003, Andrew W. Moore Support Vector Machines: Slide 39 kl kl k l ( k l Why did I tell you about this R Subject to these equivalent 0 ≤ α k ≤QP? C ∀k ∑ α k y k constraints: • It’s a formulation that QP k = 1 packages can optimize more Then define: quickly Datapoints with α k > 0 will be the support R Then classify with: w = ∑ α k y • k xBecause of further vectors jawdropping developments k k = 1 f(x,w,b) you’re = sign(w. x - b) about to learn. ..so this sum only needs b = y K (1 − ε K ) − x K . w to be over the K support vectors. where K = arg max k α k = 0 Suppose we’re in 1-dimension What would SVMs do with this data? x=0 Copyright © 2001, 2003, Andrew W. Moore Support Vector Machines: Slide 40 20
Suppose we’re in 1-dimension Not a big surprise x=0 Positive “plane” Negative “plane” Copyright © 2001, 2003, Andrew W. Moore Support Vector Machines: Slide 41 Harder 1-dimensional dataset That’s wiped the smirk off SVM’s face. What can be done about this? x=0 Copyright © 2001, 2003, Andrew W. Moore Support Vector Machines: Slide 42 21
Page 1 and 2: Support Vector Machines Note to oth
Page 3 and 4: Linear Classifiers x α f y est den
Page 5 and 6: Maximum Margin x α f y est denotes
Page 7 and 8: Computing the margin width “Predi
Page 9 and 10: Computing the margin width The line
Page 11 and 12: Learning the Maximum Margin Classif
Page 13 and 14: Learning the Maximum Margin Classif
Page 15 and 16: denotes +1 denotes -1 Uh-oh! This i
Page 17 and 18: Learning Maximum Margin with Noise
Page 19: An Equivalent QP Maximize R ∑ α
Page 23 and 24: Common SVM basis functions z k = (
Page 25 and 26: Quadratic Dot Products ⎛ ⎜ ⎜
Page 27 and 28: Higher Order Polynomials Polynomial
Page 29 and 30: Maximize QP with Quintic basis func
Page 31 and 32: VC-dimension of an SVM • Very ver
Page 33: What You Should Know • Linear SVM

Support Vector Machines - The Auton Lab

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