## Elman Network

An Elman network is a variation recurrent networks. The architecture of the network is similar to the multilayer perceptron except in the composition of the hidden layer (Figure 4). The hidden layer embodies another context layer for implementing recurrence. In this case, however, the hidden layer has recurrence and the context-hidden layer represents its own state.

In the input layer, input values at time t—1, xi(t— 1), are identified as external inputs. Concurrently, output values from the hidden layer for the previous cycle are also provided as internal inputs to the hidden layer as Ci(t—1). Initially, some small random numbers are used for internal inputs. The groups xi (t—1) and Q (t—1) consist of the total input for the hidden layer, zi(t). The sum of the linear combinations of weights and inputs, Ij(t—1), is subsequently adjusted in a nonlinear function such that Ci (t—1) = f(Ij (t—1)). The input process could be summarized as follows:

xi (t) if 1 < l < N Ci (t -1) if (N + 1) < l < L

where i = 1,2, ..., L, L = N (number of input nodes) + M (number of hidden nodes), x(t) is external input, and C(t) is context input.

The net output of the output layer is determined by the summation of the linear combination of weights and values produced from the hidden layer. As the usual process in ANNs, this is subsequently adjusted using a nonlinear function, logistic equation in this case, to

Output layer

Hidden layer

Input layer

Output layer

Hidden layer

Input layer

Context layer

Figure 4 Diagram of Elman network.

Context layer

Figure 3 Diagram of Jordan network.

### Figure 4 Diagram of Elman network.

produce output values for t. These output values are in turn compared with actual data. Weight adjustment is conducted in the same method as determined in the back-propagation algorithm. The difference between the desired output and internal output is calculated, and subsequently is back-propagated through the hidden layer down to the context and input layers.

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