Default ARTMAP 2

Gregory Amis & Gail A. CarpenterInternational Joint Conference on Neural Networks (IJCNN)

Orlando, FloridaAugust, 2007

2Geometric example: Circle-in-Square

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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

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Geometrically representedas a hyper-rectangle in the input feature space

called a category box

R

w = ( u, vc )vc = 1 − v

v

u

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TJ = M – d(RJ,a) – |RJ|

Input signal to coding node

feature 1

feat

ure

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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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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

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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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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

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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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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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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

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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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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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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