lect14

lect14 - 2 || || 2 Margin w = -≤ + •-≥ + • = 1 b x...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture outline Support vector machines
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Support Vector Machines Find a linear hyperplane (decision boundary) that will separate the data
Background image of page 2
Support Vector Machines One Possible Solution B 1
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Support Vector Machines Another possible solution B 2
Background image of page 4
Support Vector Machines Other possible solutions B 2
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Support Vector Machines Which one is better? B1 or B2? How do you define better? B 1 B 2
Background image of page 6
Support Vector Machines Find hyperplane maximizes the margin => B1 is better than B2 B 1 B 2 b 11 b 12 b 21 b 22 margin
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Support Vector Machines B 1 b 11 b 12 0 = + b x w 1 - = + b x w 1 + = + b x w - + - + = 1 b x w if 1 1 b x w if 1 ) ( x f 2 || || 2 Margin w =
Background image of page 8
Support Vector Machines We want to maximize: Which is equivalent to minimizing: But subjected to the following constraints: This is a constrained optimization problem Numerical approaches to solve it (e.g., quadratic
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
Background image of page 13
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2 || || 2 Margin w = -≤ + •-≥ + • = 1 b x w if 1 1 b x w if 1 ) ( i i i x f 2 || || ) ( 2 w w L = Support Vector Machines • What if the problem is not linearly separable? Support Vector Machines • What if the problem is not linearly separable? – Introduce slack variables • Need to minimize: • Subject to: +-≤ + •-≥ + • = i i i i 1 b x w if 1-1 b x w if 1 ) ( ξ i x f + = ∑ = N i k i C w w L 1 2 2 || || ) ( Nonlinear Support Vector Machines • What if decision boundary is not linear? Nonlinear Support Vector Machines • Transform data into higher dimensional space...
View Full Document

This document was uploaded on 10/05/2010.

Page1 / 13

lect14 - 2 || || 2 Margin w = -≤ + •-≥ + • = 1 b x...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online