5. Distance Function

y = distance (x, metric)

computes the distance between p-dimensional data points in x depending on a specified metric

The  function distance evaluates the distance between two p-dimensional vectors with respect to a specified metric. The possible metrics are given in the following table:

Distance	XploRe Name
L1	"l1"
L2	"l2", "euclid"
Maximum	"maximum"
Cosine	"cosine"
$\chi^2$	"chisquare"
Centroid	"centroid"
Tanimoto	"tanimoto"
Matching	"matching"

Several of these distances (such as Tanimoto and Matching) are designed for binary data.

The first argument of distance is the matrix, the second argument the XploRe name. By default the second argument is "l2". The commands

  x = #(1, 4)~#(1, 5)
  distance(x,"l1")

define the matrix x and evaluate the L₁ distance between the rows of that matrix:

  Contents of distance
  [1,]  0.000000  7.000000
  [2,]  7.000000  0.000000

while the command

  distance(x)

yields the L₂ distance, since the second argument of the function distance is missing:

  Contents of distance
  [1,]  0.000000  5.000000
  [2,]  5.000000  0.000000

The examples for this section are collected in matrix07.xpl.

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