In short: A matrix completion algorithm takes input values in the interval $(0,1)$. How to use this algorithm for inputs values in a larger interval?
In detail: I am working on a problem that requires recovering missing distances of a partial distance matrix. To be more specific, I have a got a set of $n$ access points $X = \{(x_1,y_1),...,(x_n,y_n)\}$ on a $2D$ plane in a $50m \times 50m$ area. The locations of the access points may change over time, and in an attempt to detect any change in their locations, real-time distance measurements (e.g., time of arrival technique) are done periodically between every pair of access points, and a Euclidean Distance Matrix (EDM) is formed. However, some of the elements in this computed EDM can be missing (e.g., two access points may go out-of-range from each other making distance measurement impossible).
We are trying to use an EDM completion algorithm "Rank alternation" proposed in Dokmanic et al.(Implementation code on GitHub) to recover the missing distances of our measured EDM (Input: a partial EDM, Output: a complete EDM). However, the algorithm only takes input values in the interval $(0,1)$, while in our measured EDM each element (i.e., distance between two access points) ranges in the interval $(0,70)$ (in meters).
We can use min-max normalization to scale the elements of our computed EDM to take values in the interval $(0,1)$. Output of the "Rank alternation" algorithm will be a complete EDM (with the missing elements recovered), and the values of its elements will be again in the interval $(0,1)$.
Is there a way to translate these values back to the distances potentially ranging in $(0,70)$?
You can alter the units of your points so that all distance values will be between $(0,1)$.
That is, if you original plane has coordinates $[0,50]\times [0,50]$, make a new coordinate system with corresponding set $[0,1/\sqrt{2}]\times [0,1/\sqrt{2}]$. So, if you original point is $(x,y)$, where $x,y\in[0,50]$, then create a new coordinate $(x',y')=(x/(50\sqrt{2}),y/(50\sqrt{2}))$. Then, the distance between each pair of points will be between $[0,1]$.
Once you have the completed distance matrix, multiply all values by $50\sqrt{2}$ to convert back to your original coordinate system.