I am confused between the Transformation and Normalization/Standardization, The basic understanding I have is Transformation: will be used in situation when we have skewness in data and to distribute the data to be like Gaussian. Normalization is used to rescale the data between 0 and 1 and make it Gaussian. what exactly does it differentiate the Transformation from Normalization?
Solved – Difference between (log, square, root) transformation and Normalization
data transformationmachine learningnormalization
Related Solutions
There are any number of smooth transformations which go through those three points.
Here are three examples:
The most obvious, as Jeremy points out in comments, is a simple linear transformation (blue in my plot above).
The red one involves a square root function (but is more complicated), and the green one involves a quadratic (it's quadratic to the left and right, but they're different quadratics which join smoothly). There's an infinite number of other functions you might choose.
We can't tell you what's best for your purposes unless you define 'best' in very specific terms.
Can you explain what properties you need to have in between the specified points?
I cannot speak in terms of machine learning, but I can speak in terms of scaling.
From our tag wiki:
tl;dr version first:
normalization refers to scaling all numeric variables in the range [0,1], such as using the formula: $$x_{new}=\frac{x-x_{min}}{x_{max}-x_{min}}$$
standardization refers to a transform to the data set to have zero mean and unit variance, for example using the equation: $$x_{new}=\frac{x-\overline{x}}{s}$$
That is, normalization does not rely on the underlying distribution; standardization transforms the data based upon the parameters of a Gaussian distribution.
Fuller explanations:
"Normalization" refers to several related processes:
("Feature scaling") A set of numbers whose maximum is $M$ and minimum is $m$ can be converted to the range from $0$ to $1$ by means of an affine transformation (which amounts to changing their units of measurement) $x \to (x-m)/(M-m)$.
A set of positive numbers $\{p_i\}$ representing probabilities or weights can be uniformly rescaled to sum to unity: divide each $p_i$ by the sum of all the $p_i$.
Analogously, a distribution (or indeed any non-negative function with a finite nonzero integral) can be normalized to have a unit integral by dividing its values by the integral.
A vector in a normed linear space is normalized (to unit length) by dividing it by its norm. This is a general procedure encompassing the two preceding operations as special examples.
The range from $0$ to $1$ can be made from $0$ to any desired limit $\alpha$ by multiplying a previously unit-normalized value by $\alpha$.
Other kinds of operations exist having a similar intent of re-expressing values in a predetermined range. Many of these are nonlinear and tend to be used in specialized settings.
Standardization:
Shifting and rescaling data to assure zero mean and unit variance.
Specifically, when $(x_i), i=1, \ldots, n$ is a batch of data, its mean is $m=(\sum_i x_i)/n$ and its variance is $s^2 = > v=(\sum_i(x_i-m)^2)/\nu$ where $\nu$ is either $n$ or $n-1$ (choices vary with application). Standardization replaces each $x_i$ with $z_i > = (x_i-m)/s$.
Best Answer
Normalization is not from the word "normal" as in normal distribution, rather it is related to a norm concept in mathematics, which is made equal to 1. Compare this to orthonormality. Hence, normalization in data science is scaling the data in a such a way that its variance becomes 1, and the mean is zero. Sometimes, it also means using the range instead of the standard deviation.
This operation does not make data normal or Gaussian. This is scaling and shifting, and Gaussian distribution remains Gaussian after this. Which means that if after normalization/standardization your data is Gaussian, then it was already Gaussian in the first place, and that all you did was make it standard normal.
What you called "transformation" is a very generic term, which includes normalization discussed above. There are some transformations that will make some data normal. For instance, the lognormal inputs data will become normal after logarithmic transformation. The Box-Cox transformation (which includes log transform) can make some data look like normal, meaning that it will be more symmetrical bell-shaped. It's not a magic wand that will make any data Gaussian though. It doesn't always work well.
Finally, in machine learning the main reason to normalize the data is not to make it like normal distribution. The reason is related to intricacies of the optimization algorithms used. It turns out that these algorithms work best when all variables (features) are in the same scale. So, you "standardize" the input data whichever way is most appropriate, such as scaling/shifting by mean and standard deviation, scaling by range to get all data into 0 to 1 interval etc.