2.7 Activation Functions of Perceptron

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 Activation Functions of Perceptron: -

The activation function applies a step rule (convert the numerical output into +1 or -1) to check if the output of the weighting function is greater than zero or not.



  • Step function gets triggered above a certain value of the neuron output; else it outputs zero.
  • Sign Function outputs +1 or -1 depending on whether neuron output is greater than zero or not.
  • Sigmoid function is the S-curve and outputs a value between 0 and 1.


Lines in 2D Space

A line in 2D space is represented by the equation (y = mx + c), where (m) is the slope, and C is the y-intercept. This can be seen as the simplest form of a decision boundary, separating the plane into two halves. In vector notation, considering vectors (a) and (b) for points on the line, the equation can be expressed as

                                a.b = 0

when the line passes through the origin, simplifying to,

Planes in 3D Space

Moving to three dimensions, a plane’s equation is.

Hyperplanes in N-Dimensional Space

Hyperplanes generalize the concept of planes to n-dimensional spaces and are crucial in separating data in machine learning models. The equation



















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