De Normalize data

Question

How would I de normalize the values which where normalized by the min max normalization below ?

Answer 1

You are referring to simple feature scaling, lets denote below the scaled $x$ as $x'$. Simple scaling translated the initial range of $x$ into $[0, 1]$ range but it can be simply recoded to any $[a, b]$ range as in your example:

$$ \frac{x - x_{(1)}}{x_{(n)} - x_{(1)}} (b + a) + a = x' $$

The process can be simply reversed by transforming $x'$ back into $[0, 1]$ range and then into new range:

$$ \frac{x' - a}{b - a} (x_{(n)} - x_{(1)}) + x_{(1)} = x $$

Simple arithmetic tells us that if $a + b = c$ then $c - b = a$ and if $gh=d$ then $d/h = g$, so there is nothing fancy in this transformation. However to reverse the scaling you have to know the initial min ($x_{(1)}$) and max ($x_{(n)}$) values because by this operation you can transform range of your data into literally any range, so you cannot deduce the initial scale from $x'$.