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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.
dist(x, method = "euclidean", diag = FALSE, upper = FALSE, p = 2)as.dist(m, diag = FALSE, upper = FALSE)
# S3 method for default
as.dist(m, diag = FALSE, upper = FALSE)
# S3 method for dist
print(x, diag = NULL, upper = NULL,
digits = getOption("digits"), justify = "none",
right = TRUE, …)
# S3 method for dist
as.matrix(x, …)
a numeric matrix, data frame or "dist"
object.
the distance measure to be used. This must be one of
"euclidean"
, "maximum"
, "manhattan"
,
"canberra"
, "binary"
or "minkowski"
.
Any unambiguous substring can be given.
logical value indicating whether the diagonal of the
distance matrix should be printed by print.dist
.
logical value indicating whether the upper triangle of the
distance matrix should be printed by print.dist
.
The power of the Minkowski distance.
An object with distance information to be converted to a
"dist"
object. For the default method, a "dist"
object, or a matrix (of distances) or an object which can be coerced
to such a matrix using as.matrix()
. (Only the lower
triangle of the matrix is used, the rest is ignored).
passed to format
inside of
print()
.
further arguments, passed to other methods.
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 do[n*(i-1) - i*(i-1)/2 + j-i]
.
The length of the vector is
The object has the following attributes (besides "class"
equal
to "dist"
):
integer, the number of observations in the dataset.
optionally, contains the labels, if any, of the observations of the dataset.
logicals corresponding to the arguments diag
and upper
above, specifying how the object should be printed.
optionally, the call
used to create the
object.
optionally, the distance method used; resulting from
dist()
, the (match.arg()
ed) method
argument.
Available distance measures are (written for two vectors
euclidean
:Usual distance between the two vectors (2
norm aka
maximum
:Maximum distance between two components of
manhattan
:Absolute distance between the two vectors (1 norm aka
canberra
:
This is intended for non-negative values (e.g., counts), in which
case the denominator can be written in various equivalent ways;
Originally, R used
binary
:(aka asymmetric binary): The vectors are regarded as binary bits, so non-zero 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
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.
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
.
# NOT RUN {
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 #-> 6-th 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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