Softmax Linearity

In the text it says: " Although softmax is a nonlinear function, the outputs of softmax regression are still determined by an affine transformation of input features; thus, softmax regression is a linear model."

Can someone explain why softmax can be determined by an affine transformation?
sin(x) and cos(x) can also be written as combination of the exponential terms, are they also affine transform? why?

Hi @mojtaba, an affine transformation is any transformation that preserves collinearity. Geometric contraction, expansion, dilation, reflection, rotation, shear, similarity transformations, spiral similarities, and translation are all affine transformations, as are their combinations. Check here for more details.

Since sin and cos are rotation, so yes they are affine transformation.

Please post your questions to specific section of our book, e.g., softmax regression. Readers who read this section may have similar question as you. :wink:

Thanks, could you please move this to the related section?

It may not be moveable. No worries, let’s leave it here!