Mathematics of Perceptrons

The perceptron algorithm is a basic artificial neuron and is considered to be a building block of neural networks. It takes inputs, applies weights and produces output using an activation function. A supervised learning algorithm, it is a binary classifier, separating data points using a linear combination of the input variables.

The algorithm consists of

  • an input vector of the form
  • a weight vector
  • a bias denoted as b
  • the summation function z
  • activation function \phi (z)

The mathematical concepts needed in order to understand the perceptron algorithm are:

  • definition of independent variables
  • what a linear equation is
  • vectors
  • dot product
  • heaviside step function

NOTE: The perceptron algorithm can classify OR and AND functions but not XOR as it is not linearly separable.

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