07 Perceptron

# 07 Perceptron - ECEN 649 Pattern Recognition Perceptrons...

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ECEN 649 Pattern Recognition Perceptrons Ulisses Braga-Neto ECE Department ECEN 649 Pattern Recognition – p.1/21

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Adjustable Discriminant Rules All the classification rules seen so far were plug-in rules, that is, they could be viewed as distribution estimation using training data. We will consider now a different idea: Assume a set of discriminants (decision boundaries) Search for the discriminant that best fits the data by optimizing some objective criterion ( “learning” ) This is the basic idea behind many popular “machine learning” classification rules: Perceptrons Support Vector Machines Neural Networks Decision Trees ECEN 649 Pattern Recognition – p.2/21
Rosenblatt’s Perceptron This was the first adjustable discriminant rule, proposed in the late 50’s by F. Rosenblatt . Assume a linear discriminant function g n ( x ) = a 0 + d s i =1 a i x i so that the designed classifier is given by ψ n ( x ) = b 1 , if a 0 + a i x i 0 0 , otherwise Adjust (“learn”) the parameters a 0 , a 1 , . . . , a d based on the training data. ECEN 649 Pattern Recognition – p.3/21

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Rosenblatt’s Perceptron - II This corresponds to the (single-layer) perceptron, depicted as follows. ECEN 649 Pattern Recognition – p.4/21
Given the feature vector x R d , consider the augmented vector: x = b 1 x B R d +1 so that the perceptron classifier is given by ψ n ( x ) = ± 1 , if a T x 0 0 , otherwise where a = [ a 0 , a 1 , . . . , a d ] T R d +1 is the parameter vector. ECEN 649 Pattern Recognition – p.5/21

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## This note was uploaded on 02/08/2010 for the course ECEN 649 taught by Professor Staff during the Spring '08 term at Texas A&M.

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07 Perceptron - ECEN 649 Pattern Recognition Perceptrons...

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