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Bidirectional associative memory (BAM) is a type of recurrent neural network. BAM was introduced by Bart Kosko in 1988. 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 neurons, 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

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 $M=\sum {}^t{X}_i{Y}_i$ where ${}^t{X}_i$ denotes the transpose. So,

$M=\left[\begin{array}{cccc}2& 0& 0& -2\\ 0& -2& 2& 0\\ 2& 0& 0& -2\\ -2& 0& 0& 2\\ 0& 2& -2& 0\\ -2& 0& 0& 2\\ \end{array}\right]$

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

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External links

• Bidirectional Associative Memory - online demo and perl source code
• Bidirectional associative memories - ACM Portal Reference