[Rd] Canberra distance
murdoch at stats.uwo.ca
Sat Feb 6 17:10:07 CET 2010
On 06/02/2010 10:39 AM, Christophe Genolini wrote:
> Hi the list,
> According to what I know, the Canberra distance between X et Y is : sum[
> (|x_i - y_i|) / (|x_i|+|y_i|) ] (with | | denoting the function
> 'absolute value')
> In the source code of the canberra distance in the file distance.c, we
> find :
> sum = fabs(x[i1] + x[i2]);
> diff = fabs(x[i1] - x[i2]);
> dev = diff/sum;
> which correspond to the formula : sum[ (|x_i - y_i|) / (|x_i+y_i|) ]
> (note that this does not define a distance... This is correct when x_i
> and y_i are positive, but not when a value is negative.)
> Is it on purpose or is it a bug?
It matches the documentation in ?dist, so it's not just a coding error.
It will give the same value as your definition if the two items have
the same sign (not only both positive), but different values if the
The first three links I found searching Google Scholar for "Canberra
distance" all define it only for non-negative data. One of them gave
exactly the R formula (even though the absolute value in the denominator
is redundant), the others just put x_i + y_i in the denominator.
None of the 3 papers cited the origin of the definition, so I can't tell
you who is wrong.
More information about the R-devel