BAM

Background

Bi-directional Associative Memory (BAM) was introduced by Kosko in 1987. It’s use of linear algebra through matrix calculations provided an easier and simpler process towards the desired network associations.

Overview

The Weight Matrix is built by taking the outer productions of the network:

The Vectors A and B need to be transformed into bi-polar vectors with the threshold function. In other words, the vector values are converted to either a 1 or a –1 by the following: 1à1 and 0à -1.

For example, given A and B matrices – we first bi-polarize the patterns. Then we calculate W above by breaking the matrices into corresponding row and column vectors and transposing one of them for the multiplication. This is done for each of the vectors, so that W= W1+ W2+ W3 if there are only 3 vectors. This means that W is computed in one shot, not through many cycles as with other models. Then we look at vector V. If it is an A-vector, then we must transpose W to calculate the B vector à W ^T V. On the other hand, if the vector V is a B vector, then we need not transpose W to calculate the A vector à W V. After calculating the desired vector, we shall apply the threshold:

If the value is < 0 à -1

> 0 à 1

= 0 à previous output

Additional Info

The Energy Surface, E, of BAM is calculated as follows:

For the continuous function, derived from Grossberg:

Where the λ determines the slope of the curve. This produces a behavior similar to the threshold.

BAM is adaptive with the following weights equation:

Interesting Points

• We can derive B from A, or A from B.
• If the input vector V is the complement of either A or B, we get its complemet à freebie!
• Missing parts in the input can be found rather easily. Just input a zero in the place of the missing data, apply the threshold function, calculate, and we find the answer. Note – the longer the vectors are, the better we are at finding missing data.
• Complements are stored by default.