Math notation, wk2, lect3

‘Feature Engineering Techniques’ (week 2, Lecture 3).

Am a bit confused by the math notation.

For Normalization, the result is said by the lecturer to be between 0 and 1: (2min 35sec).

Xnorm_screenshot

For Standardization (z-score), the result is said by the lecturer to be somewhere between 0 and the standard deviation (sigma): (4min 17sec).

Z-score_screenshot

So, why are they not the same notation (with one having 0,1 and the other 0, sigma) ?

Also, I’ve tried to find this use of the E-shaped sigma in math notation and as far as Google the search engine is showing me, it is typically to indicate membership of a set, so E-sigma{0,1} would be to indicate that is 0 or 1, not a range from 0 to 1, but also I’m not seeing the use of this with square brackets (as is in the video)… so, is Google search engine not finding this other use of sigma or is Google the company inventing its own new math notations ?

Is this funny N with round brackets (0, sigma) a standard math notation for indicating natural numbers within that range … if so, it’s wrong I think … the numbers would be real not natural… no ?

Hi @shahin
For normalization, it is guaranteed that the result is in the “interval” [0,1].
In other words:

0 <= Xnorm <= 1

If you instead choose to use standardization, you’re assuming that the distribution of data is Gaussian and the results of standardization is a Gaussian distribution with 0 mean and 1 as standard deviation.
With a Gaussian distribution, there is a fairly high probability that the value is within one standard deviation from the mean, but it is not guaranteed.
So N(0, sigma) has the meaning : Normal (Gaussian) with 0 mean and unitary standard deviation.

But you can’t guarantee that
-sigma <= Xstd <= sigma

AS a summary: in Math [0, 1] means the interval of numbers between 0, 1

0<= x <= 1

For standardization, it is wrong to use the Square bracket.

1 Like

super reply, that’s crystal clear!
thanks a lot Luigi