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CSE190, Winter 2010

Linear Discriminant Functions &

Support Vector Machines (SVM’s)

Biometrics CSE 190

Lecture 10

CSE190, Winter 2010

Announcements

•  HW2 posted.

Pattern Classification, Ch4 (Part 1)

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•  Definition

It is a function that is a linear combination of the components of x g(x) = wtx + w0 (1)

where w is the weight vector and w0 the bias

•  A two-category classifier with a discriminant function of the form (1) uses the following rule: Decide ω1 if g(x) > 0 and ω2 if g(x) < 0 ⇔ Decide ω1 if wtx > -w0 and ω2 otherwise If g(x) = 0 ⇒ x is assigned to either class

Pattern Classification, Ch4 (Part 1)

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Pattern Classification, Ch4 (Part 1)

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Pattern Classification, Ch4 (Part 1)

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Pattern Classification, Ch4 (Part 1)

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Pattern Classification, Ch4 (Part 1)

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Pattern Classification, Ch4 (Part 1)

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Pattern Classification, Ch4 (Part 1)

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Xi : inputs

Wi : weights

θ : threshold

Linear, threshold units

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The threshold can be easily forced to 0 by introducing an additional weight input W0 = θ

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CS348, Fall 2001 © David Kriegman, 2001

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CS348, Fall 2001 © David Kriegman, 2001

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CS348, Fall 2001 © David Kriegman, 2001

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CS348, Fall 2001 © David Kriegman, 2001

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CS348, Fall 2001 © David Kriegman, 2001

22 2-layer Neural Net