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.
First, is there really a bias when I would use just the (non normalized) Euclidean distance?
Second, how can I calculate something like a normalized euclidean distance on it?