I have a set of data where each data consist of $n$ different measures. For each measure, I have a benchmark value. I would like to know how close each data is to the benchmark value.
I thought of using the Weighted Euclidean Distance like this:
$\hspace{0.5in} d_{x,b}=\left( \sum_{i=1}^{n}w_i(x_i-b_i)^2)\right)^{1/2} $
where
$\hspace{0.5in}x_i$ is the value of the i-th measure for the particular data
$\hspace{0.5in}b_i$ is the corresponding benchmark value for that measure.
$\hspace{0.5in} w_i$ is the value of the weight between I will attach to the i-th measure subject to the following:
$\hspace{1in}0<w_i<1$ and $\sum_{i=1}^{n}1$
However, base on this document, I found out that the weight to use is the reciprocal of i-th measure's variance. I don't think this sort of weighting will account for the importance that I will attach to each measure.
Therefore:
Are there methods to come up with a set of weights that reflects the observer's relative importance of a measure or can the observer assign any arbitrary values for the weights?
Is it appropriate to use the Weighted Euclidean Distance to solve this problem?