Support Vector Machines - The Auton Lab

More documents

Recommendations

Info

Specifying a line and margin “Predict Class = +1” zone “Predict Class = -1” zone Plus-Plane Classifier Boundary Minus-Plane • How do we represent this mathematically? • …in m input dimensions? Copyright © 2001, 2003, Andrew W. Moore Support Vector Machines: Slide 11 Specifying a line and margin • Plus-plane = { x : w . x + b = +1 } • Minus-plane = { x : w . x + b = -1 } Classify as.. “Predict Class = +1” zone wx+b=1 wx+b=0 wx+b=-1 +1 -1 Universe explodes “Predict Class = -1” zone if if if Plus-Plane Classifier Boundary Minus-Plane w . x + b >= 1 w . x + b
Computing the margin width “Predict Class = +1” zone wx+b=1 wx+b=0 wx+b=-1 “Predict Class = -1” zone M = Margin Width How do we compute M in terms of w and b? • Plus-plane = { x : w . x + b = +1 } • Minus-plane = { x : w . x + b = -1 } Claim: The vector w is perpendicular to the Plus Plane. Why? Copyright © 2001, 2003, Andrew W. Moore Support Vector Machines: Slide 13 Computing the margin width “Predict Class = +1” zone wx+b=1 wx+b=0 wx+b=-1 “Predict Class = -1” zone • Plus-plane = { x : w . x + b = +1 } • Minus-plane = { x : w . x + b = -1 } Claim: The vector w is perpendicular to the Plus Plane. Why? And so of course the vector w is also perpendicular to the Minus Plane M = Margin Width How do we compute M in terms of w and b? Let u and v be two vectors on the Plus Plane. What is w . ( u – v ) ? Copyright © 2001, 2003, Andrew W. Moore Support Vector Machines: Slide 14 7
Page 1 and 2: Support Vector Machines Note to oth
Page 3 and 4: Linear Classifiers x α f y est den
Page 5: Maximum Margin x α f y est denotes
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 and 20: An Equivalent QP Maximize R ∑ α
Page 21 and 22: Suppose we’re in 1-dimension Not
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

Create successful ePaper yourself

Delete template?

Save as template?