ABSTRACT

A Hopfield network classifies different categories of inputs according to their basin of attraction: two classes are considered equivalent if they have the same attractor. We have seen that this classification depends on the choice of a measure of closeness in the sense of the Hamming distance. In fact, although the choice of this measure may be of interest in some cases, it is not necessarily relevant in others. In the field of pattern recognition, for example, one is chiefly interested in invariants: two shapes are considered equivalent if they only differ by a translation, although their Hamming distance can be very large.