Introduction. I have an Euclidean distance between two subsequences $A_{i,m}$ and $A_{j,m}$, that start, respectively, at $i$ and $j$, and have length $m$. We can write this Euclidean distance by using the $L^{2}-$norm:
$\left\lVert A_{i,m}-A_{j,m} \right\rVert_{2} \overset{\mathrm{def}}{=} \sqrt{\sum_{k=0}^{m-1}\left(a_{i+k}-a_{j+k}\right)^{2}}$
However, I would like to write the z-normalized form, i.e. $\sqrt{\sum_{k=0}^{m-1}\left(\frac{a_{i+k}-\mu_i}{\sigma_i}-\frac{a_{j+k}-\mu_j}{\sigma_j}\right)^{2}}$, of the previously mentioned Euclidean norm:
Question. What symbol or sign can I use to indicate the z-normalization in the Euclidean norm? Something like the following? (that I do not like)
$\left\lVert A_{i,m}-A_{j,m} \right\rVert_{2}^{z-normalization}$