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 class 'default': 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, ...))
- a numeric matrix, data frame or
- the distance measure to be used. This must be one of
"minkowski". Any unambiguous substring can be given.
- logical value indicating whether the diagonal of the distance matrix should be printed by
- logical value indicating whether the upper triangle of the distance matrix should be printed by
- 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).
- digits, justify
- passed to
- right, ...
- further arguments, passed to other methods.
Available distance measures are (written for two vectors x and y):
- Usual square distance between the two vectors (2 norm).
- Maximum distance between two components of x and y (supremum norm)
- Absolute distance between the two vectors (1 norm).
- 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 non-negative values (e.g. counts): taking the absolute value of the denominator is a 1998 R modification to avoid negative distances.
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
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
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
The lower triangle of the distance matrix stored by columns in a vector, say
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*(i-1) - i*(i-1)/2 + j-i]. The length of the vector is n*(n-1)/2, i.e., of order n^2.
The object has the following attributes (besides
"class" equal to
- integer, the number of observations in the dataset.
- optionally, contains the labels, if any, of the observations of the dataset.
- Diag, Upper
- logicals corresponding to the arguments
upperabove, specifying how the object should be printed.
- optionally, the
callused to create the object.
- optionally, the distance method used; resulting from
dist(), the (
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.
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 <- 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 <- 1e100 stopifnot(dist(cbind(x, y), method = "canberra") == print(dist(cbind(x1, y), method = "canberra"))) ## 2) y <- 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
Documentation reproduced from R 3.0.2. License: GPL-2.