Improve Euclidean distance similarity calculation
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Key: MAHOUT-847
URL: https://issues.apache.org/jira/browse/MAHOUT-847
Project: Mahout
Issue Type: Improvement
Components: Collaborative Filtering
Affects Versions: 0.5
Reporter: Sean Owen
Assignee: Sean Owen
Priority: Minor
Fix For: 0.6
In the non-distributed recommender world, the Euclidean distance similarity is
calculated as n/(1+d), where d is distance and n is dimension. 1/(1+d) is a
valid mapping from distance [0,infinity) to similarity (0,1]. n is there to
"correct" for the fact that things are farther apart in higher dimensions. It
would be right-er, after some discussion, to use a factor of sqrt(n), and apply
directly to the distance; 1/(1+d/sqrt(n)).
I propose fixing the calculation accordingly.
In the distributed similarity, the formula is 1-1/(1+d), which is the wrong way
around. That will be fixed. I'd apply the same heuristic, except that at the
moment we don't have access to the value of n at that point. I don't like the
inconsistency but it's minor; would rather get this change in now, which
definitely improves things.
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