I have a single neuron with 2 inputs, and identity activation, where f is activation function and u is output:

$u = f(w_1x_1 + w_2x_2 + b) = w_1x_1 + w_2x_2 + b$

My guessing for the separation line equation:

$u = w_1x_1 + w_2x_2 + b$
$\implies x_2 = \dfrac{u - w_1x_1 - b}{w_2}$
$\implies x_2 = (\dfrac{-w_1}{w_2})x_1 + \dfrac{u-b}{w_2}$

And the questions are:

1) Is the separation line equation above correct?

2) And when f is not identity function, is the separation line equation still the same? or different?


1 Answer 1


I found the answer, the output u is not related to plotting x2 against x1 here, coz u is like z axis and seeing the separation line is looking perpendicularly to the x1x2 plane, and whatever u value is, it's just a dot.

Put u as zero for the solving steps in the question.

So the separation line equation is this (with any activation function):

$x_2 = \dfrac{-w_1}{w_2}x_1 + \dfrac{-b}{w_2}$


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