Download a = hardlims

3
An
Illustrative
Example
1
3
Apple/Orange Sorter
Neural
Network
Sensors
Sorter
Shape: {1 : round ; -1 : elliptical}
Texture: {1 : smooth ; -1 : rough}
Weight: {1 : > 1 lb. ; -1 : < 1 lb.}
Apple
Orange
2
Prototype Vectors
3
sensors：
p =
Shape: {1 : round ; -1 : elliptical}
Texture: {1 : smooth ; -1 : rough}
Weight: {1 : > 1 lb. ; -1 : < 1 lb.}
shape
te xture
w eight
3
3
Perceptron
a = -1, n < 0
hardlims：
a = 1, n ≧0
4
3
Perceptron (cont.)
i.e. W = [-1,1]T
(p1, p2) = (-1,2), then n = 2
a = hardlims(2) = 1
(p1, p2) = (1,-3), then n = -5
a = hardlims(-5) = -1
5
3
Apple/Orange Example
6
3
Apple/Orange Example
橘子
7
3
Hamming Network
8
3
Feedforward Layer
For Orange/Apple Recognition
S=2
purelin：a=n
9
3
Feedforward Layer (cont.)
Why is it called Hamming ? The Hamming distance
between two vectors is equal the number of elements
that are different.
e.g. the Hamming distance between [1,-1,-1] and [1,1,1] is 2 ,
the Hamming distance between [1,1,-1] and [1,1,1] is 1
10
3
Recurrent Layer
a = 0, n < 0
poslims：
a= n, n ≧0
11
3
Hamming Operation
First Layer：input
12
3
Hamming Operation
Second Layer： ε＝0.5

 posl in  1 – 0.5 4 




–
0.5
1
2


a 2 1  = p osl in  W2 a 2 0  = 

3
 posli n   = 3

0
0


 posl in  1 – 0.5


 –0.5 1

2
2
2
a 2  = p osl in  W a 1  = 



 posl in  3  =

 –1.5 

3

0
3
0
橘子
13
3
Hopfield Network
14
3
Apple/Orange Problem
satlins：
a = -1, n <-1
a = n, -1≦n ≦1
a = 1, 1<n
15
3
Apple/Orange Problem
Test：
橘子
16
Summary
3
• Perceptron
– Feedforward Network
– Linear Decision Boundary
– One Neuron for Each Decision
• Hamming Network
–
–
–
–
Competitive Network
First Layer – Pattern Matching (Inner Product)
Second Layer – Competition (Winner-Take-All)
# Neurons = # Prototype Patterns
• Hopfield Network
– Dynamic Associative Memory Network
– Network Output Converges to a Prototype Pattern
– # Neurons = # Elements in each Prototype Pattern
17