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Let $v$ : a $k$-dimensional vector of positive real values.

The function is given by:

$$ f(v)_i = \frac{v_i}{\sum_{j=1}^k v_j}$$

What is this function called?

How does compare to the Softmax function?

I was inspired by the Softmax function, but I thought this keeps the proportions in a way that Softmax doesn't.

Example:

v = [1,2,3] 
softmax(v) = [0.09..., 0.24..., 0.6...]
this(v) = [0.16..., 0.33..., 0.5]
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  • $\begingroup$ Softmax of the logs? $\endgroup$
    – p.s.
    Oct 2, 2016 at 17:33
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    $\begingroup$ Normalization of v. $\endgroup$
    – zyx
    Oct 2, 2016 at 17:34

1 Answer 1

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The $\mathcal L^1$ norm of a $k$-dimensional vector is defined as: $$\Vert v\Vert_{1}=\sum_{i=1}^{k} |v_i|$$ So as mentioned in the comments, your function normalizes each vector with respect to its $\mathcal L^1$ norm, i.e. $$\Vert f(v)\Vert_{1}=1,\,\forall v$$

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