What is the name for normalization $\leq 1$? In my current thesis I have two weight components. As I want to join those components, weighted by a percentage, I thought about normalizing(/scaling?) both components respectively by their max value.
Component $c1$ will therefore be:
$c1' = \frac{c1}{\max(c1)}$
respectively component $c2$
$c2' = \frac{c2}{\max(c2)}$
As I now have to write about it I can't find the correct term for this normalizing/scaling.
In short what is the name of normalizing/scaling process:
$$x' = \frac{x}{\max(x)}$$
 A: If the minimum value of both $c1$ and $c2$ is zero, then this is known as "min-max scaling":
$$x' = \frac{x - x_{min}}{x_{max} - x_{min}}$$
This normalizes the variable range to $[0,1]$. Note that, depending on the variable range, a linear transformation to the range $[0,1]$ might not be appropriate (another occasionally used scaling function is the exponential function).
Another normalization method is "z score standardization", which normalizes to zero mean and variance one (and thus SD one too):
$$x' = \frac{x-\mu}{\sigma}$$
A: There is no specific name for this normalization, as far as I know....
I think, for a thesis, it is enough to mention that data were normalized because this is most probably marginal information and the reviewer should understand the process without providing more details.
If you want to be clearer, when your data are positive, you can say "Data were normalized to be between 0 and 1". When you have negative values, the normalized values will be between -1 and +1 and the max should be taken in absolute value.
