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?


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):

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


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.