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'''Bidirectional associative memory''' ('''BAM''') is a type of [[recurrent neural network]]. BAM was introduced by [[Bart Kosko]] in 1988.<ref>http://sipi.usc.edu/~kosko/BAM.pdf</ref> There are two types of associative memory, auto-associative 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 [[Hopfield network]] in that they are both forms of [[associative memory]]. However, Hopfield nets return patterns of the same size.


== Topology ==
A BAM contains two layers of [[neuron]]s, 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.


==Procedure==
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===Learning===
Imagine we wish to store two associations, A1:B1 and A2:B2.
* A1 = (1, 0, 1, 0, 1, 0), B1 = (1, 1, 0, 0)
* A2 = (1, 1, 1, 0, 0, 0), B2 = (1, 0, 1, 0)
 
These are then transformed into the bipolar forms:
* X1 = (1, -1, 1, -1, 1, -1), Y1 = (1, 1, -1, -1)
* X2 = (1, 1, 1, -1, -1, -1), Y2 = (1, -1, 1, -1)
 
From there, we calculate <math>M = \sum{{}^t \! X_i Y_i}</math> where <math>{}^t \! X_i</math> denotes the transpose.
So,
 
<math>M = \left[ {\begin{array}{*{10}c}
  2 & 0 & 0 & -2  \\
  0 & -2 & 2 & 0  \\
  2 & 0 & 0 & -2  \\
  -2 & 0 & 0 & 2  \\
  0 & 2 & -2 & 0  \\
  -2 & 0 & 0 & 2  \\
\end{array} } \right]</math>
 
===Recall===
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.
 
==See also==
* [[Autoassociative memory]]
* [[Self-organizing feature map]]
 
==References==
{{reflist|2}}
 
== External links ==
* [http://www.lwebzem.com/cgi-bin/res/nnbam.cgi Bidirectional Associative Memory - online demo and perl source code]
* [http://portal.acm.org/citation.cfm?id=46936# Bidirectional associative memories - ACM Portal Reference]
 
[[Category:Neural networks]]

Latest revision as of 00:42, 11 July 2014


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