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This model is also the extension of McCulloch-Pitts neuron model. Two stages are used to illustrate ANN with continuous characteristics. The schematic diagram of the model is presented in Figure 2.5. The linear combination of input values is calculated in the first stage. The weight value associated with each value of the input array lies between 0 and 1. The summation function can be expressed as σ in Equation (2.4).

(2.4)

where

T ≡ extra input value associated with weight value 1 which represents the threshold or bias of a neuron.

Figure 2.3 Linear threshold function.

Figure 2.4 Schematic diagram of linear threshold gate.

The second stage of the model is the activation function which takes the sum-of-product value as the input and produces the output. The activity of this stage determines the characteristic of the ANN model. This function compresses the amplitude of the output so that it lies in the range of [0, 1] or [−1, 1]. The compression of the output signal is performed to mimic the signal produced by biological neuron in the form of continuous action-potential spikes.

The function used in the above discussed model is semi-linear and termed as logistic sigmoid function. The graphical depiction of the function is presented in Figure 2.6. The mathematical demonstration of logistic sigmoid function is presented in Equation (2.5).

(2.5)

Figure 2.5 ANN model with continuous characteristics.

Figure 2.6 Graphical representation of logistic sigmoid function.

From the graphical representation, it is clear that for the large positive value of input x, the output value y tends to 1. On the other hand, for the negative value of x, y tends to 0. Again, if x approaches to −∞ or ∞, the slope of the graph becomes 0. The increment of slope occurs as x goes close to 0. These characteristics of the sigmoid graph are very crucial in ANN.