{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

chapter4 - Chapter 4 Multilayer Perceptron Multilayer...

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

View Full Document Right Arrow Icon
Chapter 4 Multilayer Perceptron
Background image of page 1

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

View Full Document Right Arrow Icon
Chapter 4 --- Multilayer Perceptron 2 Multilayer Perceptron ring2 A generalization of the single-layer perceptron to enhance its computational power. ring2 Training method : error backpropagation algorithm which is based on the error- correction learning rule. ring2 Requirement : nonlinear neuronal function should be smooth (i.e., differentiable everywhere ).
Background image of page 2
Chapter 4 --- Multilayer Perceptron 3 Multilayer Perceptron
Background image of page 3

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

View Full Document Right Arrow Icon
Chapter 4 --- Multilayer Perceptron 4 Backpropagation Training Algorithm ring2 A systematic method for training multilayer ANN, error is back ward propagated to adjust the weights during training phase. Therefore it s called backpropagation training. ring2 Requires that the nonlinear neuronal function be differentiable everywhere . A good choice is the sigmoid function (or logistic / squashing function)
Background image of page 4
Chapter 4 --- Multilayer Perceptron 5 Backpropagation Training Algorithm ring2 Training Objective : to adjust the weights so that application of a set of inputs produces the desired set of outputs. ring2 Belongs to the category of Supervised Learning.
Background image of page 5

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

View Full Document Right Arrow Icon
Chapter 4 --- Multilayer Perceptron 6 Graphical Representation
Background image of page 6
Chapter 4 --- Multilayer Perceptron 7 Mathematical Analysis ring2 Consider neuron j , ring2 Define error signal e j ( n ) = d j ( n ) - y j ( n ) ring2 Define instantaneous squared error for output neuron j = ring2 Instantaneous sum of squared errors of the network where the summation is over all output neurons. v n w n y n and y n v n j ji i i j j ( ) ( ) ( ) ( ) ( ( )) = = ϕ 1 2 2 e n j ( ) E n e n j j ( ) ( ) = 1 2 2
Background image of page 7

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

View Full Document Right Arrow Icon
Chapter 4 --- Multilayer Perceptron 8 Mathematical Analysis Make use of the steepest gradient descent concept, where local gradient points to the required changes in synaptic weights. E n w n E n e n e n y n y n v n v n w n ji j j j j j j ji ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = = ⋅- ⋅ e n v n y n j j i ( ) ( ( )) ( ) ' 1 ϕ Δ w n E n w n n y n ji ji j i ( ) ( ) ( ) ( ) ( ) = - = η ηδ δ ϕ j j j n e n v n ( ) ( ) ( ( )) ' = ---- (4.1)
Background image of page 8
Chapter 4 --- Multilayer Perceptron 9 Mathematical Analysis If neuron j is an output neuron Easy, as we know the target value of output neurons. e j ( n ) = d j ( n ) - y j ( n ) ---- (4.2) ---- (4.3) = Δ ) ( ) ( ) ( n y j neuron of signal input n gradient local parameter rate learning n w correction Weight i j ji δ η δ ϕ j j j n e n v n ( ) ( ) ( ( )) ' =
Background image of page 9

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

View Full Document Right Arrow Icon
Chapter 4 --- Multilayer Perceptron 10 Mathematical Analysis If neuron j is a hidden neuron Difficult, as there s no target value for hidden neurons. We have to calculate δ ϕ j j j j j j n E n y n y n v n E n y n v n ( ) ( ) ( ) ( ) ( ) ( ) ( ) '( ( )) = - = -
Background image of page 10
Chapter 4 --- Multilayer Perceptron 11 Mathematical Analysis = - = = j j kj k k k k k k y w v and v d e n e n E ) ( , ) ( 2 1 ) ( 2 ϕ E n y n e n e n v n v n y n j k k k k k j ( ) ( ) ( ) ( ) ( ) ( ) ( ) = = ⋅- e n v n v n y n k k k k j ( ) ( ( )) ( ) ( ) ' ϕ = - δ k kj k n w n ( ) ( ) δ ϕ δ j j k kj k n v n n w n ( ) ( ( )) ( ) ( ) ' = --- (4.4)
Background image of page 11

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

View Full Document Right Arrow Icon
Chapter 4 --- Multilayer Perceptron 12 Mathematical Analysis Error backward
Background image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}