Perceptrons

Abstract

The perceptron [38], also referred to as a McCulloch-Pitts neuron or linear threshold gate, is the earliest and simplest neural network model. Rosenblatt used a single-layer perceptron for the classification of linearly separable patterns. For a one-neuron perceptron, the network topology is shown in Fig. 1.2, and the net input to the neuron is given by net = J 1 i=1 w i x i − θ = w T x − θ, (3.1) where all the symbols are as explained in Sect. 1.2. The one-neuron perceptron using the hard-limiter activation function is useful for classification of vector x into two classes. The two decision regions are separated by a hyperplane w T x − θ = 0, (3.2) where the threshold θ is a parameter used to shift the decision boundary away from the origin. The three popular activation functions are the hard limiter (threshold) function, φ(x) = 1, x ≥ 0 −1(or 0), x < 0 , (3.3) the logistic function φ(x) = 1 1 + e −βx , (3.4)