Familiarity Discrimination

For the computation of the reliability of the the answer for the heteroassociation a backward projection of the associative memory is required [12]. The backward projection corresponds to a bidirectional associative memory (BAM) [20]. This time the learned matrix is cued with the retrieved vector and the best address vector is retrieved. Formally, y is the address vector, and the retrieved vector which should be determined is x^l. The categorization rule for the determination of the retrieved vector x^l is:

This means that the synaptic matrix used is a transposition of the matrix which is used for the forward projection. T* is the threshold of the unit. The threshold is set to the maximum sum ∑j=1mwijyj:

Let x be the question vector and y the retrieved vector that was determined by the associative memory for example by a part of the associative memory. First, the vector x^l which belongs to the vector y is determined. These two vectors form together a vector pair x^l y which is stored in the associative memory. It was either created by learning, x^l and y were learned together, or created through overlap with other already learned vector pairs. The vector x^l is determined by a backward projection of the vector y. In the second step, the similarity of the stored address vector x^l to the actually presented vector x is determined. The greater the similarity of the vector x^l to the vector x, the more reliable the retrieved vector y. We can measure the similarity by the Hamming distance function

or by the scalar product

that measure of the projection of one vector onto another.

For auto-association the task there is no need for a backward projection. In the case of auto-association n = m. We can measure the similarity by the scalar product with

and

since W is symmetric with n = m. This is equivalent to the quadratic form

The quadratic form can be as well be interpreted as the energy function [13]

The threshold operation to determine similarity sim is applied to the scalar value net,

with the threshold

sim = 1 indicates that the question vector x was stored in the associative memory, sim = 0 that is was not. This operation called the familiarity discrimination, in familiarity discrimination there is no need per se to extract the whole answer pattern [13]. In the following we will only preform auto-association.