This function computes and returns the distance matrix computed by using the specified distance measure to compute the distances between the rows of a data matrix.
1 2 3 4 5 6 7 8 9 10 11 12 13  dist(x, method = "euclidean", diag = FALSE, upper = FALSE, p = 2)
as.dist(m, diag = FALSE, upper = FALSE)
## Default S3 method:
as.dist(m, diag = FALSE, upper = FALSE)
## S3 method for class 'dist'
print(x, diag = NULL, upper = NULL,
digits = getOption("digits"), justify = "none",
right = TRUE, ...)
## S3 method for class 'dist'
as.matrix(x, ...)

x 
a numeric matrix, data frame or 
method 
the distance measure to be used. This must be one of

diag 
logical value indicating whether the diagonal of the
distance matrix should be printed by 
upper 
logical value indicating whether the upper triangle of the
distance matrix should be printed by 
p 
The power of the Minkowski distance. 
m 
An object with distance information to be converted to a

digits, justify 
passed to 
right, ... 
further arguments, passed to other methods. 
Available distance measures are (written for two vectors x and y):
euclidean
:Usual distance between the two vectors (2 norm aka L_2), sqrt(sum((x_i  y_i)^2)).
maximum
:Maximum distance between two components of x and y (supremum norm)
manhattan
:Absolute distance between the two vectors (1 norm aka L_1).
canberra
:sum(x_i  y_i / x_i + y_i). Terms with zero numerator and denominator are omitted from the sum and treated as if the values were missing.
This is intended for nonnegative values (e.g., counts): taking the absolute value of the denominator is a 1998 R modification to avoid negative distances.
binary
:(aka asymmetric binary): The vectors are regarded as binary bits, so nonzero elements are ‘on’ and zero elements are ‘off’. The distance is the proportion of bits in which only one is on amongst those in which at least one is on.
minkowski
:The p norm, the pth root of the sum of the pth powers of the differences of the components.
Missing values are allowed, and are excluded from all computations
involving the rows within which they occur.
Further, when Inf
values are involved, all pairs of values are
excluded when their contribution to the distance gave NaN
or
NA
.
If some columns are excluded in calculating a Euclidean, Manhattan,
Canberra or Minkowski distance, the sum is scaled up proportionally to
the number of columns used. If all pairs are excluded when
calculating a particular distance, the value is NA
.
The "dist"
method of as.matrix()
and as.dist()
can be used for conversion between objects of class "dist"
and conventional distance matrices.
as.dist()
is a generic function. Its default method handles
objects inheriting from class "dist"
, or coercible to matrices
using as.matrix()
. Support for classes representing
distances (also known as dissimilarities) can be added by providing an
as.matrix()
or, more directly, an as.dist
method
for such a class.
dist
returns an object of class "dist"
.
The lower triangle of the distance matrix stored by columns in a
vector, say do
. If n
is the number of
observations, i.e., n < attr(do, "Size")
, then
for i < j ≤ n, the dissimilarity between (row) i and j is
do[n*(i1)  i*(i1)/2 + ji]
.
The length of the vector is n*(n1)/2, i.e., of order n^2.
The object has the following attributes (besides "class"
equal
to "dist"
):
Size 
integer, the number of observations in the dataset. 
Labels 
optionally, contains the labels, if any, of the observations of the dataset. 
Diag, Upper 
logicals corresponding to the arguments 
call 
optionally, the 
method 
optionally, the distance method used; resulting from

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.
Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979) Multivariate Analysis. Academic Press.
Borg, I. and Groenen, P. (1997) Modern Multidimensional Scaling. Theory and Applications. Springer.
daisy
in the cluster package with more
possibilities in the case of mixed (continuous / categorical)
variables.
hclust
.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46  require(graphics)
x < matrix(rnorm(100), nrow = 5)
dist(x)
dist(x, diag = TRUE)
dist(x, upper = TRUE)
m < as.matrix(dist(x))
d < as.dist(m)
stopifnot(d == dist(x))
## Use correlations between variables "as distance"
dd < as.dist((1  cor(USJudgeRatings))/2)
round(1000 * dd) # (prints more nicely)
plot(hclust(dd)) # to see a dendrogram of clustered variables
## example of binary and canberra distances.
x < c(0, 0, 1, 1, 1, 1)
y < c(1, 0, 1, 1, 0, 1)
dist(rbind(x, y), method = "binary")
## answer 0.4 = 2/5
dist(rbind(x, y), method = "canberra")
## answer 2 * (6/5)
## To find the names
labels(eurodist)
## Examples involving "Inf" :
## 1)
x[6] < Inf
(m2 < rbind(x, y))
dist(m2, method = "binary") # warning, answer 0.5 = 2/4
## These all give "Inf":
stopifnot(Inf == dist(m2, method = "euclidean"),
Inf == dist(m2, method = "maximum"),
Inf == dist(m2, method = "manhattan"))
## "Inf" is same as very large number:
x1 < x; x1[6] < 1e100
stopifnot(dist(cbind(x, y), method = "canberra") ==
print(dist(cbind(x1, y), method = "canberra")))
## 2)
y[6] < Inf #> 6th pair is excluded
dist(rbind(x, y), method = "binary" ) # warning; 0.5
dist(rbind(x, y), method = "canberra" ) # 3
dist(rbind(x, y), method = "maximum") # 1
dist(rbind(x, y), method = "manhattan") # 2.4

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