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perceptron1 - Simple Perceptrons Simple Perceptrons Perform...

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Simple Simple Perceptrons Perceptrons
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PR , ANN, & ML 2 Simple Perceptrons xrhombus Perform supervised learning boxshadowdwn correct I/O associations are provided xrhombus Feed-forward networks boxshadowdwn connections are one-directional xrhombus One layer boxshadowdwn input layer + output layer
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PR , ANN, & ML 3 boxshadowdwn N : dimension of the input vector boxshadowdwn M : dimension of the output vector boxshadowdwn inputs boxshadowdwn real outputs boxshadowdwn weight vectors boxshadowdwn activation function N j x j ,..., 1 , = M i y i ,..., 1 , = w i M j N ij , ,..., , ,..., = = 1 1 g 1 x 2 x 3 x 4 x 1 y 2 y 3 y w 34 = = = N j j ij i i x w g net g y 1 ) ( ) ( Notations
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PR , ANN, & ML 4 Perceptron Training xrhombus given boxshadowdwn input patterns boxshadowdwn desired output patterns boxshadowdwn how to adapt the connection weights such that the actual outputs conform the desired outputs u x u O M i y O u i u i , , 1 L = =
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PR , ANN, & ML 5 Simplest case xrhombus two types of inputs xrhombus binary outputs (-1,1) xrhombus thresholding 1 x 2 x ( , ) w w 1 2 u o u u w x w x w y x w = + + = ) sgn( ) sgn( 2 2 1 1
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PR , ANN, & ML 6 Examples 2 x 1 x 2 x O 0 0 -1 0 1 -1 1 0 -1 1 1 1 1 x 2 x w w 1 1 = w 2 1 = w 0 15 = . O 1 x 2 x O 0 0 -1 0 1 1 1 0 1 1 1 -1 ) 5 . 1 sgn( ) ( 2 2 1 1 - + = u u x w x w net g 2 x 2 x 1 x 1 x 1 x 2 x
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PR , ANN, & ML 7 Linear separability xrhombus Is it at all possible to learn the desired I/O associations?
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