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This site does not describe the nature of the tag. How does it differ from re-scaling? Many authors use the two terms interchangeably. I can not understand normalization's operational meaning.

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Re-scaling means that you multiply your variable by a factor, i.e. $x \to x/a$. A normalization is a specific kind of re-scaling, where the factor $a$ is such that the values of $x$ become of order one. Its form depends on the context and what you are trying to do. Examples are $a= \langle x \rangle$ or $a= \textrm{max}(x)$. Perhaps the most common one is when you do $x \to (x-\langle x \rangle)/\sigma$, because if $x$ follows a Gaussian distribution, the re-scaled variable follows a normal distribution (average 0 and std 1). Note, this last transformation actually involves a re-scaling, but also a translation.

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  • $\begingroup$ what does "your variable" mean ? what's x and a ? $\endgroup$ – Subhash C. Davar Feb 21 at 22:27
  • $\begingroup$ "Your variable" means a random variable your aim to re-scale. $x$ is the random variable. $a$ is the factor. $\endgroup$ – kastellane Feb 22 at 1:30
  • $\begingroup$ Gaussian distribution is also called normal distribution. It is the standard normal distribution that produces mean of deviations equal to zero and variance equal to 1. Terming it re-scaling or normalization is incorrect. $\endgroup$ – Subhash C. Davar Feb 23 at 14:37
  • $\begingroup$ In which sense $x \to (x-\langle x \rangle)/\sigma$ is not a re-scaling (after a translation) and, more specifically, a normalization? $\endgroup$ – kastellane Feb 23 at 16:45
  • $\begingroup$ If a=⟨x⟩ = mean, and its division by standard deviation , it generates probability /normal distribution - perhaps also called standard score distribution/standard normal distribution. Re-scaling the data entails observed data minus minimum score and division by maximum Range of data. It is different from mathematical statistics. $\endgroup$ – Subhash C. Davar Feb 24 at 0:23

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