Value range of normalization methods? min-max, z-score, decimal scaling I am working my way through Normalization (data transformation) of data and was curious about four methods: 


*

*min-max normalization, 2. z-score, 3. z-score mean absolute deviation, and 4. decimal scaling.  


I am reading through a book so this is difficult to understand but it seems to me that the first three normalization methods output to a value range between 0 and 1 and the last with a range of -1 to 1.
Am I understanding this correctly or is the range of values different?
Reference: Data Mining Concepts and Techniques
In the book it mentions: 

To help avoid dependence on the choice of measurement units, the data should be normalized.  This involves transforming the data to fall within a smaller or common range such as [-1,1] or [0.0-1.0].

As you can see it says "common range" so I am not sure if that means what i mentioned above for the different methods or if it can actually be "anything"
 A: Min-Max-Scaling means that one linearly transforms real data values such that the minimum and the maximum of the transformed data take certain values -- frequently 0 and 1 or -1 and 1. This depends on the context. For example the formula
$
x^\prime := (x-x_{\min})/(x_{\max} -x_{\min} )
$
does the job for the values 0 and 1. Here $x_{\min}$ is the minimal data value appearing and similarly $x_{\max}$.
The z-score linearly transforms the data in such a way, that the mean value of the transformed data equals 0 while their standard deviation equals 1. The transformed values themselves do not lie in a particular interval like [0,1] or so. The transformation formula thus is:
$
x^\prime := (x-\overline{x})/s
$
where $\overline{x}$ denotes the mean value of the data and $s$ its standard deviation.
A: I am working on this problem as well for my data mining class.
range for min-max is [new min, new max] or commonly [0.0, 1.0] or [ -1.0, 1.0 ].
range for z-score using std dev is [ - infinity, infinity ] although it is very unlikely to get extreme values.
range for z-score using mean absolute deviation should be the same as the other z-score.
range for decimal scaling is [ -1, 1 ].
This is what I have answered, and I think I got it right, but I would have troubles proving it for the z-score.
