BAM(Bidirectional Associative Memory)

Question

Suppose [1 0 0 1 0 1] <--> [0 0 0 1], this is a association then in implementing BAM, why we convert 0 to -1 and then calculate weight matrix.

Answer 1

The fundamental reason why 0 are unsuitable for BAM storage is that 0's in binary patterns are ignored when added, but -1's in bipolar patterns are not: 1+0=1 but 1+(-1)=0. If the numbers are matrix entries that represent synaptic strengths, then multiplying and ass in binary quantities can only produce excitatory connections.

Meanwhile multiplying and add in bipolar quantities produces excitatory and inhibitory connections. The connections strengths represent the frequency of excitatory and inhibitory connections int the individual correlation matrices.

Refer:

• http://sipi.usc.edu/~kosko/BAM.pdf "Bidirectional Associative Memory, Bart Kosko"

Answer 2

In testing, the goal is to verify if our weight matrix is correct. In forward testing, the Y matrices will be multiplied with the weights to obtain corresponding X matrices. In backward testing, the X matrices will be multiplied with the weights to obtain corresponding Y matrices. I will be using the bipolar activation function, which will categorize the values <= 0 as -1 and values > 0 as 1.

This is because, considering the given sets A and B, the value domain consists of 1 and -1. Hence, this is the only activation function where f(x) = {-1, 1} for any x. BIPOLAR ACTIVATION FUNTION

IN SHORT BECAUSE WE USE BI-POLAR ACTIVATION FUNCTION WE NEED -1