[MAHOUT-847] Improve Euclidean distance similarity calculation

• Type: Improvement
• Status: Closed
• Priority: Minor
• Resolution: Fixed
• Affects Version/s: 0.5
• Fix Version/s: 0.6
• Labels: distance euclidean similarity vector
• Assignee: Sean R. Owen
• Reporter: Sean R. Owen
• Due: 27/Oct/11
• Created: 20/Oct/11 13:21
• Updated: 31/Jan/24 22:11
• Resolved: 21/Oct/11 09:20

Description

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, and apply directly to the distance; 1/(1+d/sqrt).

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.