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How to calculate normalized euclidean distance on two vectors?

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Let's say I have the following two vectors:
x = [(10-1).*rand(7,1) + 1; randi(10,1,1)]; y = [(10-1).*rand(7,1) + 1; randi(10,1,1)];
The first seven elements are continuous values in the range [1,10]. The last element is an integer in the range [1,10].
Now I would like to compute the euclidean distance between x and y. I think the integer element is a problem because all other elements can get very close but the integer element has always spacings of ones. So there is a bias towards the integer element.
How can I calculate something like a normalized euclidean distance on it?

Accepted Answer

Andrei Bobrov
Andrei Bobrov on 3 Jul 2016
Edited: Andrei Bobrov on 3 Jul 2016
out = sqrt(sum((x-y).^2)/numel(x))
out = norm(x-y)/sqrt(numel(x))
  1 Comment
Sepp on 3 Jul 2016
Thank you for your answer. Do you know if there is really a bias in my example if I would take just the normal Euclidean distance?

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