Programming = assign proper weights

1

• Programming assign proper weights
• Learning

u1
Wi,1
Wi,2
u2
ui
Wi,n
un
n
Oi f ( S Wj i uj )
Activation
j1
f transfer function (usually non-linear
threshold function, sigmoid, hyperbolic tangent,
etc.)
2
Perceptron
Rosenblatt, 1962, Minsky, 1969
W1
X1
W2
Oi
X2
Wn
Xn
1, if S Wi xi gt q
Activation Oi
0, if S Wi xilt q
W0
-q
1
W1
Oi
X1
1, if S Wi xi gt 0
Activation Oi
Wn
Xn
0, if S Wi xilt 0
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Algorithm for Perceptron Learning

• Initialize (w0, w1,.., wn) randomly.
• Iterate through training set collecting
  unclassified examples by current weights.
• If all examples correctly classified (or up to an
  acceptable threshold classified) then quit
• else
• compute sum of misclassified examples, x,
• S S x, if failed to fire while it should
• S S - x, if fired while it shouldnt
• 4. Modify weights wt1 wt k S.

4
Perceptron learning
Total input in w0 w1 x1 w2 x2
w1
w0
x1
In 0
x2

w2
w2
Decision surface
Learning locating proper decision surface
5
To find decision surface use gradient descent
methods
E ( W1,W2) error function sum of distances of
unclassified input vectors from decision surface
E (W1,W2)
W1
W2
6
Cannot do XOR problem
Can do it with multi layer
-1.5
1
-0.5
1
1.0
-9.0
x1
1.0
x1
1.0
1.0
x2
x2
Perceptron training doesnt work (Minsky-Papert)
7
Back Propagation
1
1
Output
1 e Swij xj
0
Can get stuck in local minima .
Slow speed of learning
(Boltzman machine uses simulated annealing for
search and doesnt get stuck)
8
o1
o2
oi
W11
W23
Wij
v1
v3
v2
vj
w11
w32
wjk
zk
Binary or continuous
?1
?2
Output of vj Vjm g( hjm) g(S wjk zkm)
k
Output of oi Oim g( him) g(S Wi j Vjm)
g(S Wij g(S w j k
zkm) )
j
j
k
2
Error function E (w) ½ S
zim -g(S Wij g(S wjk zkm) )
Continuous , differentiable.
g(h) 1 / (1 e 2h ) or tanh (h)
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To get weights
D Wij -n q
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• Judd , 1988
• Teaching nets is NP- Complete on of nodes.
• Possible Solution
• Use probabilistic algorithms to train them
  (like GAs).

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Example back propagation network

• Input Vector 19 bits correspond to a person
• 1 0 1 0 1
  0 1 . Etc.
• Output vector 5 bits
• 0 1 0 0
  0
• Training and testing data vectors
• 24-bits each
• 80-training
• 20- testing

Mets fan
Likes lemonade
From chicago
From NY
Cubs fan
Democrat
republican
NY Jets fan
Likes tennis
Beans fan
NY yankees fan
White sox fan
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• Possible rules from data
• People from Chicago are never fans of NY teams
• 50 of Cub fans are White Sox fans
• All Mets fans are Jets fans.
• Can train BP-network to learn such patterns.
• After training , testing given an input
• 1010000 0
• We get output 0.44 0.88 0.23 0.03 0.02
• i.e. There is a small chance that person likes
  Sox, high probability that likes Beans, no chance
  that he likes Mets, Jets or tennis.

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• Input A Democrat Cubs fan
• Output 0.11 0.88 0.14 0.01 0.02
• Input A Republican Cubs fan
• Output 0.77 o.92 0.13 0.05 0.02
• So, Republican cubs fans also like the sox white
  Democrats do not.
• Input A Chicagoan who doesnt like Cubs
• Output 0.17 0.26 0.79 0.05 0.04
• He likes tennis
• ( Fuzzy rules)