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I am trying to understand this paper, but in this paper the following || symbol is frequently used.

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$$p_i(j) \propto \exp \{ - \| A x_i - A x_j \|_2^2\}$$

I wonder to know what does it mean, what are these two 2 are doing here?

And also wonder to know does the above || symbol has different meaning than the below || symbol (considering there is only one 2 here)?

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$$p_i(j) \propto \exp \left\{ -\dfrac{\|x_i - x_j\|^2}{2 \sigma_i^2} \right\}$$

Thanks in advance.

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    $\begingroup$ $||\cdot||$ is the norm. See en.wikipedia.org/wiki/Norm_%28mathematics%29 $\endgroup$ – Alex Silva Jan 15 '15 at 16:20
  • $\begingroup$ what are those two 2? $\endgroup$ – dariush Jan 15 '15 at 16:23
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    $\begingroup$ The lower $2$ probably means it's the 2-norm (the standard euclidean distance), and the upper is probably just an exponent. $\endgroup$ – Henrik Jan 15 '15 at 16:24
  • $\begingroup$ Machine learning: because notation is fun! $\endgroup$ – Emily Jan 15 '15 at 16:50

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