Distance calculation/vector range significance I'm trying to implement item based collaborative filtering. Do any distance calculations allow for weighting of certain ranges of values within each vector? 

For example, I would like to be able to say values 10..22 within each vector are more significant than values within the range 0..10. 

I've been experimenting with Pearson, Tanimoto and Euclidean algorithms, but they all seem to assume equal weighting for each value within the vector.

Am I approaching this problem in the right way, and if not, how do others deal with this problem?
I created a scoring system ("Thomas Scoring System") to deal with this problem.  If you treat "distance" as a similarity score, this system should work for you. http://exploringpossibilityspace.blogspot.com/2014/02/thomas-scoring-system.html


  Here's Thomas Scoring System (TSS) in a nutshell: Treat each metric and their values as evidence that weigh for or against specific values in the performance index. This is an inference process and not an arithmetic calculation, as in the Usual Method. The output of TSS is an estimation of the Weight of Evidence for all index values.  The Weight of Evidence can be expressed as a probability distribution, where all the evidence weights sum to one.


To use your example, each range is a condition: A) 10 &lt;= x &lt;= 22; and B) x &lt; 10. If A is true, then it weighs in favor of certain similarity (distance) scores.  If B is true, then it weights in favor of other similarity (distance) scores, but would have less weight compared to other evidence.