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From "Lance Norskog (Issue Comment Edited) (JIRA)" <j...@apache.org>
Subject [jira] [Issue Comment Edited] (MAHOUT-847) Improve Euclidean distance similarity calculation
Date Thu, 20 Oct 2011 23:26:10 GMT

    [ https://issues.apache.org/jira/browse/MAHOUT-847?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13132191#comment-13132191
] 

Lance Norskog edited comment on MAHOUT-847 at 10/20/11 11:24 PM:
-----------------------------------------------------------------

As a perpetual beginner, it is daunting to learn Mahout. It helps if well-defined math terms
are only used when the code matches the (200-year-old) concept. 

Perhaps _WarpedEuclideanSimilarity_ would be more clear?
                
      was (Author: lancenorskog):
    As a perpetual beginner, it is daunting to learn Mahout. It helps if well-defined math
terms are only used when the code matches the (200-year-old) concept. 

WarpedEuclideanSimilarity perhaps would be more clear.
                  
> Improve Euclidean distance similarity calculation
> -------------------------------------------------
>
>                 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
>              Labels: distance, euclidean, similarity, vector
>             Fix For: 0.6
>
>         Attachments: MAHOUT-847.patch
>
>
> 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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