By Kroese B., van der Smagt P.

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5). All connections are weighted. In 1982, Hopfield (Hopfield, 1982) brings together several earlier ideas concerning these networks and presents a complete mathematical analysis based on Ising spin models (Amit, Gutfreund, & Sompolinsky, 1986). It is therefore that this network, which we will describe in this chapter, is generally referred to as the Hopfield network. 5) which update their activation values asynchronously and independently of other neurons. All neurons are both input and output neurons.

There are two problems associated with storing too many patterns: 1. the stored patterns become unstable; 2. , stable states which do not correspond with stored patterns). The first of these two problems can be solved by an algorithm proposed by Bruce et al. (Bruce, Canning, Forrest, Gardner, & Wallace, 1986): Algorithm 1 Given a starting weight matrix W = wjk , for each pattern xp to be stored and each element xpk in xp define a correction ǫk such that ǫk = 0 1 if yk is stable and xp is clamped; otherwise.

A somewhat similar method is known as frequency sensitive competitive learning (Ahalt, Krishnamurthy, Chen, & Melton, 1990). In this algorithm, each neuron records the number of times it is selected winner. The more often it wins, the less sensitive it becomes to competition. Conversely, neurons that consistently fail to win increase their chances of being selected winner. Cost function Earlier it was claimed, that a competitive network performs a clustering process on the input data.