default artmap 2
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Default ARTMAP 2
Gregory Amis & Gail A. CarpenterInternational Joint Conference on Neural Networks (IJCNN)
Orlando, FloridaAugust, 2007
2Geometric example: Circle-in-Square
x
y
0 1
1
Task: Discriminate points INSIDE the circle from points OUTSIDE the circle
Using training data like
3ARTMAP Geometry
Long-term memory weight vector for coding node:
feature 1
feature 2
0 1
01
Geometrically representedas a hyper-rectangle in the input feature space
called a category box
R
w = ( u, vc )vc = 1 − v
v
u
4
TJ = M – d(RJ,a) – |RJ|
Input signal to coding node
feature 1
feat
ure
2
Input signal to coding node J: Choice-by-difference rule
Input signal TJ is greatest for box closest to input a
If point a is in multiple boxesthe smallest box gets greatest signal
a
d(R1,a)
|R3|
R1
R3
R2
R4
d(R4,a)
# input features 0.01
city-block distance box size
Measure of similarity between coding node weights and input patternDetermines which coding nodes learn and contribute to class prediction
51st training pair creates point box
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0
a(1)
No coding nodes/boxes exist
First input:class training pair (a(1),IN) presented.
R1
u1 = v1 = a(1)
Recruit new coding node,
Fast commit learning sets w1 = A, u1 = v1 = a(1) creates point box R1 at a
6
u1new = u1
old a(2) = u1old
v1new = v1
old a(2) = a(2)
u1 = v1 = a(1)
2nd pair expands existing box
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0
a(2)
Existing box R1 matches a(2) well enough
Second training pair (a(2),IN) presented.
R1Fast learning
expands R1 to include a(2)
R1
R1 a
7
Existing box R1 matches a(3) well enoughbut it’s the wrong class
Match tracking raises vigilanceresets R1
3rd pair creates new OUT point box
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0 1
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0
a(3)
New node recruitedcreating OUT point box R2
Third training pair (a(3),OUT) presented.
R1R2
84th point extends OUT box
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0 1
1
0
a(4)
Fourth training pair (a(4),OUT) presented.
Existing box R1 matches a(4) well enoughbut it’s the wrong class
Match tracking raises vigilanceresets R1
R2 winspasses vigilance
because |R2a| |R1a| and learns
R2
R1
95th pair creates new OUT point box
x
y
0 1
1
0
a(5)
Fifth training pair (a(5),OUT) presented.
R2
Existing box R1 matches a(5) well enoughbut it’s the wrong class
Match tracking resets R1 R2 wins, but fails vigilance
|R2a| > |R1a|
New node recruitedcreating OUT point box R3
R3
R1
106th pair expands R3
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y
0 1
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0
Sixth training pair (a(6),OUT) presented.
R2
R1
Existing box R1 matches a(5) well enoughbut it’s the wrong class
Match tracking resets R1 R2 wins, but fails vigilance
R3 wins, passes vigilance and learns
R3
a(6)
R3
11At this point…
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Classification PatternWinner-Take-All
Distributed Activation
R1
R2
R3
127th pair fails next input test!
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a(7)
Classification PatternWinner-Take-All
Distributed Activation
Predicts a(7) is INCorrect!
Still thinks a(7) is OUT
Wrong!
Seventh training pair (a(7),IN) presented.
No matter how many times a(7) is presented,Default ARTMAP 1 will never correct this mistake!
R1
R2
R3
13Default ARTMAP 2 learns on a(7)
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0 1
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Distributed Activation
Predicts a(7) is INCorrect!
Seventh training pair (a(7),IN) presented. Checks distributed next-input test: fails
Match tracking raises vigilanceresets R1
a(7)
New coding node recruitedcreates point box R4
Passes next-input test!R4
R1
R2
R3
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