[EDIT] After a second read, the proposed normalization looks non standard. Suppose that $m\le x \le M$ ($m$ and $M$ denote the min and max). The scaling factor will be, depending on the situation:
- if $m\le M\le 0$: $-m$,
- if $m\le 0\le M$, and $|m|\ge M$: $-m$
- if $m\le 0\le M$, and $|m|\le M$: $M$
- if $0\le m\le M$: $M$
It turns out to be (if I do not err) the largest of the absolute values of $m$ or $M$.
A more standard writing, more symmetric, could be:
x_max = max([abs(max(x)), abs(min(x))]);
x_max = max(abs(x));
This computes the maximum
x_max in absolute amplitude. This corresponds to an $\ell_\infty$ norm dispersion-type. Then you center $x$ around the mean (in some $\ell_2$ sense), then divide by the above maximum
If $\mu$ denotes the mean, you will end up:
- for the first two cases, in $[\mu/m-1,\mu/m-M/m]$
- for the last two cases, in $[m/M-\mu/M,1-\mu/M]$
And there is not a lot more I can say, without more information. If the extrema values are sufficiently symmetric around the mean, with a close-to-$0$ average, the outcomes would lay around the $[-1,1]$ interval, because $M/m \approx -1 $ and $\mu/M$ or $\mu/m$ are close to $0$. But you could have different behaviors: if $m=-10$, $M=1$, $\mu=-9$, you will have
x_norm in $[-0.1,1]$.
But if the mean is $0.5$, the interval would be $[-1.05,0.05]$.
Variable reduction is something one could take classically as an input to a decorrelating or source separation technique; a PCA for instance, or related tools (SVD, independent component analysis) for instance.
But subtracting the central location (here the average) before computing extremas and rescaling a dispersion after that is more standard.
And however, mixing different norms in normalization is not the practice I would recommend. So:
- subtracting the mean and dividing by the (residual) standard deviation
- subtracting the median and dividing by the MAD (median absolute deviation)
- subtracting the midrange and dividing by the max or min of the residual (ie the half range)
- mapping the values between fixed bounds, such as $[0,1]$
are much more common.