Re: Under what condition is Mahalanobis distance OPTIMAL?

cramer_at_unc.edu
Date: 08/15/04 

Date: 14 Aug 2004 23:25:26 -0400

In sci.stat.math b83503104 <b83503104@yahoo.com> wrote:
: There are so many kinds of distance metrics.
: Is there a way one can show under what conditions the Mahalanobis
: distance is the optimal distance metric?
There is no such thing as optimal

: At least, it is intuitively correct that Mahalanobis distance is
: better than Euclidean distance when the axes have different weighting,
: or when the axes are correlated.
yes if you use appropriate weighting

: Can it be formulated mathematically exactly under which conditions it
: is optimal?
: Thanks

Relevant Pages

  • Re: Combining multiple parameters as DOE response
    ... > of a designed experiment. ... I've used Mahalanobis-Taguchi methods to ... My first thought was to then calculate a Mahalanobis ... > treatment based on the Mahalanobis distance. ...
    (sci.stat.math)
  • Re: Under what condition is Mahalanobis distance OPTIMAL?
    ... There are so many kinds of distance metrics. ... Is there a way one can show under what conditions the Mahalanobis ... better than Euclidean distance when the axes have different weighting, ...
    (sci.stat.math)
  • Re: Performing computation of distance Mahalanobis
    ... I found that it exists in Matlab a fonction for computing directly the distance of Mahalanobis. ... I discovered myself in Statistic Toolbox the Mahalanobis distance. ...
    (comp.soft-sys.matlab)
  • Mahalanobis distance
    ... Can someone please clarify for me which is the formula for the Mahalanobis ... where S^-1 the inverse of the covariance matrix and m the mean of the ... M=sumwhere b are the parameters of the PCA and lamda the ... However, I have seen formula for the Mahalanobis distance, with the ...
    (sci.image.processing)
  • Re: distance distribution between similar images
    ... distribution of the distance (which may be Euclidean, Mahalanobis or city block) between the two? ... Or, another way of putting it is: If I have two images that are just white noise, what is the distribution of the distance between the two? ...
    (sci.image.processing)