0
$\begingroup$

In binary classification, if we can transform the softmax function (needs 2 outputs) to sigmoid function (needs 1 output):

$$\begin{align*}\mathrm{Pr}(Y=0|X)&=\frac{e^{b_0\cdot X}}{e^{b_0 \cdot X}+e^{b_1 \cdot X}}\\ &=\frac{e^{(b_0-b_1)\cdot X}}{e^{(b_0-b_1) \cdot X}+e^{(b_1-b_1) \cdot X}}\\ &=\frac{e^\beta}{e^{\beta \cdot X}+1}\end{align*}$$ $$\begin{align*}\mathrm{Pr}(Y=1|X)&=\frac{e^{b_1\cdot X}}{e^{b_0 \cdot X}+e^{b_1 \cdot X}}\\ &=\frac{e^{(b_1-b_1)\cdot X}}{e^{(b_0-b_1) \cdot X}+e^{(b_1-b_1) \cdot X}}\\ &=\frac{1}{e^{\beta \cdot X}+1}\end{align*}$$

Why don't we do similar things in multiclass classification, and transform the original softmax function which needs K (K being number of classes) outputs to another that only needs (K-1) outputs?

$\endgroup$

Your Answer

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

Browse other questions tagged or ask your own question.