CS621: Artificial Intelligence Lecture 14: perceptron training

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CS621 Artificial IntelligenceLecture 14
perceptron training

• Pushpak Bhattacharyya
• Computer Science and Engineering Department
• IIT Bombay

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The Perceptron Model A perceptron is a
computing element with input lines having
associated weights and the cell having a
threshold value. The perceptron model is
motivated by the biological neuron.
Output y
Threshold ?
w1
wn
Wn-1
x1
Xn-1
3
y
1
?
Swixi
Step function / Threshold function y 1 for
Swixi gt? 0 otherwise
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Perceptron Training Algorithm (PTA)

• Preprocessing
• The computation law is modified to
• y 1 if ?wixi gt ?
• y o if ?wixi lt ?
• ?

w3
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PTA preprocessing cont

• 2. Absorb ? as a weight
• ?
• 3. Negate all the zero-class examples

x1
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Example to demonstrate preprocessing

• OR perceptron
• 1-class lt1,1gt , lt1,0gt , lt0,1gt
• 0-class lt0,0gt
• Augmented x vectors-
• 1-class lt-1,1,1gt , lt-1,1,0gt , lt-1,0,1gt
• 0-class lt-1,0,0gt
• Negate 0-class- lt1,0,0gt

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Example to demonstrate preprocessing cont..

• Now the vectors are
• x0 x1 x2
• X1 -1 0 1
• X2 -1 1 0
• X3 -1 1 1
• X4 1 0 0

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Perceptron Training Algorithm

• Start with a random value of w
• ex lt0,0,0gt
• 2. Test for wxi gt 0
• If the test succeeds for i1,2,n
• then return w
• Modify w, wnext wprev xfail
• Goto 2

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Tracing PTA on OR-example

• wlt0,0,0gt wx1 fails
• wlt-1,0,1gt wx4 fails
• wlt0,0,1gt wx2 fails
• wlt-1,1,1gt wx4 fails
• wlt0,1,1gt wx4 fails
• wlt1,1,1gt wx1 fails
• wlt0,1,2gt wx4 fails
• wlt1,1,2gt wx2 fails
• wlt0,2,2gt wx4 fails
• wlt1,2,2gt success

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Theorems on PTA

1. The process will terminate
2. The order of selection of xi for testing and
   wnext does not matter.