527:
The internal matrix has n x p independent degrees of freedom, where n is the dimension of the first vector (6 in this example) and p is the dimension of the second vector (4). This allows the BAM to be able to reliably store and recall a total of up to min(n,p) independent vector pairs, or min(6,4)
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To retrieve the association A1, we multiply it by M to get (4, 2, -2, -4), which, when run through a threshold, yields (1, 1, 0, 0), which is B1. To find the reverse association, multiply this by the transpose of M.
75:, which we shall denote X and Y. Layers X and Y are fully connected to each other. Once the weights have been established, input into layer X presents the pattern in layer Y, and vice versa.
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and hetero-associative. BAM is hetero-associative, meaning given a pattern it can return another pattern which is potentially of a different size. It is similar to the
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defines the state of a BAM. To store a pattern, the energy function value for that pattern has to occupy a minimum point in the energy landscape.
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The layers can be connected in both directions (bidirectional) with the result the weight matrix sent from the X layer to the Y layer is
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proved to correspond to a local minimum of the energy function. The discrete BAM is proved to converge to a stable state.
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528:= 4 in this example. The capacity can be increased above by sacrificing reliability (incorrect bits on the output).
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It is said to be bi-directional as it can respond to inputs from either the input or the output layer.
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NEURAL NETWORKS, FUZZY LOGIC AND GENETIC ALGORITHM: SYNTHESIS AND APPLICATIONS (WITH CD)
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is presented to BAM, the neurons change states until a bi-directionally stable state
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Bidirectional
Associative Memory – Python source code for the Wiki article
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and the weight matrix for signals sent from the Y layer to the X layer is
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The stability analysis of a BAM is based on the definition of
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Imagine we wish to store two associations, A1:B1 and A2:B2.
125:. Thus, the weight matrix is calculated in both directions.
57:. However, Hopfield nets return patterns of the same size.
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Bidirectional associative memories – ACM Portal
Reference
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RAJASEKARAN, S.; PAI, G. A. VIJAYALAKSHMI (2003-01-01).
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for the bidirectional case, which for a particular case
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The memory or storage capacity of BAM may be given as
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in 1988. There are two types of associative memory,
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901:IEEE Transactions on Systems, Man, and Cybernetics
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156:X2 = (1, 1, 1, -1, -1, -1), Y2 = (1, -1, 1, -1)
153:X1 = (1, -1, 1, -1, 1, -1), Y1 = (1, 1, -1, -1)
504:" is the number of units in the X layer and "
8:
797:Hopfield's Auto-associative Energy Function
145:A2 = (1, 1, 1, 0, 0, 0), B2 = (1, 0, 1, 0)
142:A1 = (1, 0, 1, 0, 1, 0), B1 = (1, 1, 0, 0)
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712:The Energy Function proposed by Kosko is
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207:{\displaystyle M=\sum {\!X_{i}^{T}Y_{i}}}
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894:"Bidirectional Associative Memories"
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28:Bidirectional associative memory
18:Bidirectional Associative Memory
849:{\displaystyle E(A,B)=-AMA^{T}}
762:{\displaystyle E(A,B)=-AMB^{T}}
50:in that they are both forms of
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698:{\displaystyle (A_{f},B_{f})}
71:A BAM contains two layers of
871:Self-organizing feature map
246:denotes the transpose. So,
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1006:Artificial neural networks
962:. PHI Learning Pvt. Ltd.
477:{\displaystyle \min(m,n)}
239:{\displaystyle X_{i}^{T}}
160:From there, we calculate
627:. When a paired pattern
38:. BAM was introduced by
36:recurrent neural network
426:{\displaystyle M=\left}
866:Autoassociative memory
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118:{\displaystyle W^{T}}
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934:www.wileyindia.com
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969:978-81-203-2186-1
588:{\displaystyle E}
573:Lyapunov function
517:{\displaystyle m}
497:{\displaystyle n}
91:{\displaystyle W}
16:(Redirected from
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937:. Retrieved
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52:associative
939:2020-08-15
877:References
40:Bart Kosko
828:−
741:−
532:Stability
484:, where "
395:−
380:−
345:−
335:−
300:−
285:−
174:∑
129:Procedure
1000:Category
860:See also
799:. (i.e.
445:Capacity
134:Learning
67:Topology
536:A pair
73:neurons
966:
436:Recall
214:where
55:memory
897:(PDF)
707:Kosko
964:ISBN
909:doi
856:).
457:min
32:BAM
1002::
948:^
932:.
921:^
905:18
903:.
899:.
884:^
972:.
942:.
915:.
911::
842:T
838:A
834:M
831:A
825:=
822:)
819:B
816:,
813:A
810:(
807:E
783:B
780:=
777:A
755:T
751:B
747:M
744:A
738:=
735:)
732:B
729:,
726:A
723:(
720:E
693:)
688:f
684:B
680:,
675:f
671:A
667:(
647:)
644:B
641:,
638:A
635:(
615:)
612:B
609:,
606:A
603:(
583:E
556:)
553:B
550:,
547:A
544:(
512:m
492:n
472:)
469:n
466:,
463:m
460:(
420:]
413:2
408:0
403:0
398:2
388:0
383:2
375:2
370:0
363:2
358:0
353:0
348:2
338:2
330:0
325:0
320:2
313:0
308:2
303:2
295:0
288:2
280:0
275:0
270:2
263:[
259:=
256:M
232:T
227:i
223:X
199:i
195:Y
189:T
184:i
180:X
171:=
168:M
111:T
107:W
86:W
30:(
20:)
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