Why weights are not squared in the weighted Euclidean distance formula?

Question

I am working on Data Mining and need distance between data points.

With two points $(x_1, y_1), (x_2, y_2)$ & weights $w_1$ and $w_2$ respectively. The euclidean distance is: $$ \sqrt{w_1\times(x_2-x_1)^2+w_2\times(y_2-y_1)^2}. $$ I think intuitively $w_1$ & $w_2$ were supposed to be squared as they are getting square rooted in the result.

Answer 1

You are right. $w$ is just a name for $\frac{1}{s^2}$, where $s$ for standard deviation. Full answer here:

http://www.econ.upf.edu/~michael/stanford/maeb4.pdf