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"
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.