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I would like to apply the sigmoid (logistic) function:

$\sigma{(x)} = \frac{1}{1+e^{-x}}$

to a vector $\mathbb{R}^n$ or matrix $\mathbb{R}^{m × n}$.

And the question is how to write this function for vectors/matrices. I need it for a scientific publication.

Vadim
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  • Oftentimes people simply write $\sigma(\mathbf{x})$ to denote elementwise application of $\sigma$ to the vector or matrix (so if $\mathbf{x} = \begin{bmatrix} x\ y\ z\end{bmatrix}$, then $\sigma(\mathbf{x})=\sigma\left(\begin{bmatrix} x\ y\ z\end{bmatrix}\right) = \begin{bmatrix}\sigma(x)\ \sigma(y) \ \sigma(z)\end{bmatrix}$ for example). If in doubt, maybe you could just quickly explain the notation you are using. – Minus One-Twelfth Mar 01 '19 at 10:54
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    Please answer the question, I will accept your answer. – Vadim Mar 01 '19 at 10:59

1 Answers1

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Oftentimes, people simply write $\sigma(\mathbf{x})$ to denote elementwise application of the sigmoid function to a vector or matrix. (For example, the author does it here, search the page for "vectorizing".) If in doubt, maybe you could just quickly explain the notation you are using.

Minus One-Twelfth
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