Default ARTMAP 2

1. Gregory Amis & Gail A. CarpenterInternational Joint Conference on Neural Networks (IJCNN) Orlando, Florida August, 2007 Default ARTMAP 2

2. 0 1 Geometric example: Circle-in-Square Task: Discriminate points INSIDE the circle from points OUTSIDE the circle 1 Using training data like y x

3. ARTMAP Geometry Long-term memoryweight vector for coding node: 1 feature 2 v w = ( u, vc ) vc = 1 − v R u Geometrically represented as a hyper-rectangle in the input feature space called a category box 0 0 1 feature 1

4. Input signal to coding node Measure of similarity between coding node weights and input pattern Determines which coding nodes learn and contribute to class prediction Input signal to coding node J: Choice-by-difference rule city-block distance box size R4 TJ = M – d(RJ,a) – |RJ| R1 d(R4,a) R2 feature 2 d(R1,a) # input features 0.01 Input signal TJ is greatest for box closest to input a If point a is in multiple boxesthe smallest box gets greatest signal R3 |R3| a feature 1

5. 0 1 1st training pair creates point box First input:class training pair (a(1),IN)presented. No coding nodes/boxes exist 1 Recruit new coding node, Fast commit learningsets w1 = A, u1 = v1 = a(1) creates point box R1 at a y R1 a(1) u1 = v1 = a(1) 0 x

6. 0 1 2nd pair expands existing box Second training pair (a(2),IN)presented. Existing box R1matches a(2) well enough 1 a(2) v1new = v1old a(2) =a(2) R1 a y R1 Fast learningexpands R1 to include a(2) R1 u1 = v1 = a(1) u1new = u1old a(2) =u1old 0 x

7. 0 1 3rd pair creates new OUT point box Third training pair (a(3),OUT)presented. Existing box R1matches a(3) well enoughbut it’s the wrong class Match tracking raises vigilance resets R1 1 a(3) y R2 R1 New node recruitedcreating OUT point box R2 0 x

8. 0 1 4th point extends OUT box Fourth training pair (a(4),OUT)presented. Existing box R1matches a(4) well enoughbut it’s the wrong class Match tracking raises vigilance resets R1 1 R1 y R2 R2 winspasses vigilance because |R2a|  |R1a| and learns a(4) 0 x

9. 0 1 5th pair creates new OUT point box Fifth training pair (a(5),OUT)presented. Existing box R1matches a(5) well enoughbut it’s the wrong class 1 a(5) R3 Match tracking resets R1R2 wins, but fails vigilance |R2a| > |R1a| R1 y R2 New node recruitedcreating OUT point box R3 0 x

10. 0 1 6th pair expands R3 Sixth training pair (a(6),OUT)presented. Existing box R1matches a(5) well enoughbut it’s the wrong class 1 R3 R3 Match tracking resets R1R2 wins, but fails vigilance R1 y a(6) R2 R3 wins, passes vigilance and learns 0 x

11. 0 1 At this point… Classification Pattern Winner-Take-All 1 R3 R1 y R2 Distributed Activation 0 x

12. 0 1 7th pair fails next input test! Classification Pattern Winner-Take-All Seventh training pair (a(7),IN)presented. 1 Predicts a(7)isIN Correct! R3 R1 a(7) y R2 Distributed Activation 0 Still thinks a(7)isOUT Wrong! x No matter how many times a(7) is presented,Default ARTMAP 1 will never correct this mistake!

13. 0 1 Default ARTMAP 2 learns on a(7) Seventh training pair (a(7),IN)presented. Checks distributed next-input test: fails Match tracking raises vigilance resetsR1 1 R3 New coding node recruitedcreates point box R4 R1 a(7) y R2 R4 Passes next-input test! Distributed Activation 0 Predicts a(7)isIN Correct! x