2.3.1 The McCulloch-Pitts Model of Neuron

The early model of an artificial neuron is introduced by Warren McCulloch and Walter Pitts in 1943. The McCulloch-Pitts neural model is also known as linear threshold gate. It is a neuron of a set of inputs $I_1, I_2, I_3, ..., I_m$ and one output $y$. The linear threshold gate simply classifies the set of inputs into two different classes. Thus the output $y$ is binary. Such a function can be described mathematically using these equations:

$$Sum = \mathop{\sum_{i = 1}^{N}}{I_{i} W_{i}},$$ (2.1)

$$y = f(Sum).$$ (2.2)

$W_1, W_2, W_3, ..., W_m$ are weight values normalized in the range of either $(0,1)$ or $(-1,1)$ and associated with each input line, $Sum$ is the weighted sum, and $T$ is a threshold constant. The function $f$ is a linear step function at threshold $T$ as shown in figure 2.3. The symbolic representation of the linear threshold gate is shown in figure 2.4 [Has95].

Figure 2.3: Linear Threshold Function

Figure 2.4: Symbolic Illustration of Linear Threshold Gate

The McCulloch-Pitts model of a neuron is simple yet has substantial computing potential. It also has a precise mathematical definition. However, this model is so simplistic that it only generates a binary output and also the weight and threshold values are fixed. The neural computing algorithm has diverse features for various applications [Zur92]. Thus, we need to obtain the neural model with more flexible computational features.