-Artificial%20Neural%20Network-%20Chapter%204

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-Artificial Neural Network-Chapter 4

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Outline

• ADALINE-------------------------------------------
  ------- 2
• MADALINE------------------------------------------
  ------ 6
• Least-Square Learning Rule -----------------------
  -- 7
• The proof of Least-Square Learning Rule -------
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ADALINE

• ADALINE(Adaptive Linear Neuron) is a network
  model proposed by Bernard Widrow in1959.

single processing element
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Method

• Method ? The value in each unit must 1 or 1
  
• net

This is different from perception's transfer
function.
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Method
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MADALINE

• MADALINE It is composed of many ADALINE
• (Multilayer Adaline.)

• if more than half of netj 0,then
• output 1,otherwise, output -1

• After the second layer, the majority vote is used.

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Least-Square Learning Rule (1/2)

• Least-Square Learning Rule

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Least-Square Learning Rule (2/2)

• By applying the least-square learning rule the
  weights is

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Exercise Use Adaline (1/4)
X1 X2 X3 Tj
X1 1 1 0 1
X2 1 0 1 1
X3 1 1 1 -1
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• Sol. First calculate R

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• Verify the net
• ??(1,1,0) net3X1-2X2-2X31 Y1 ok
• ??(1,0,1) net3X1-2X2-2X31 Y1 ok
• ??(1,1,1) net3X1-2X2-2X3-1 Y-1 ok

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Proof of Least Square Learning Rule(1/3)

• Let us use Least Mean Square Error to ensure the
  minimum total error. As long as the total error
  approaches zero, the best solution is found.
  Therefore, we are looking for the minimum oflt
  gt?
• Proof

mean of ltTk2gt
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Proof of Least Square Learning Rule(2/3)
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Proof of Least Square Learning Rule(3/3)
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