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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:

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

$\displaystyle y = f(Sum).$ (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
\begin{figure}
\centerline {\epsfysize=1.8in \epsfbox{./figures/figThreshold.epsi}}\end{figure}

Figure 2.4: Symbolic Illustration of Linear Threshold Gate
\begin{figure}
\centerline {\epsfysize=2.0in \epsfbox{./figures/figLTU.epsi}}\end{figure}

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.


next up previous
Next: 2.3.2 The Perceptron Up: 2.3 Artificial Neural Networks Previous: 2.3 Artificial Neural Networks
Kiyoshi Kawaguchi
2000-06-17