For nearest neighbor problems in d-dimensional real spaces, image002ai, we use three popular Minkowski image004ai distance metrics:

 

The Manhattan (image006ai ),
The Euclidean ( image008ai) and
The Max (image010ai ).

 

A Minkowski distance metric, image004ai, in a d-dimensional real space between two vectors, image012ai and image014ai, is defined as

 

image016ai               Eq. (1)

 

On the limiting case,  image018ai, (image010ai ), Eq. (1) reduces to

 

image020ai

 

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