Distance Matrix Computation
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) "as.dist"(m, diag = FALSE, upper = FALSE)"print"(x, diag = NULL, upper = NULL, digits = getOption("digits"), justify = "none", right = TRUE, ...)"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 distance between the two vectors (2 norm aka $L_2$), $sqrt(sum((x_i - y_i)^2))$.
- Maximum distance between two components of $x$ and $y$ (supremum norm)
- Absolute distance between the two vectors (1 norm aka $L_1$).
- $sum(|x_i - y_i| / |x_i + y_i|)$. Terms with zero numerator and denominator are omitted from the sum and treated as if the values were missing.
- (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.
- The $p$ norm, the $p$th root of the sum of the $p$th powers of the differences of the components.
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.
Inf values are involved, all pairs of values are
excluded when their contribution to the distance gave
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
"dist" method of
can be used for conversion between objects of class
and conventional distance matrices.
as.dist() is a generic function. Its default method handles
objects inheriting from class
"dist", or coercible to matrices
as.matrix(). Support for classes representing
distances (also known as dissimilarities) can be added by providing an
as.matrix() or, more directly, an
for such a class.
- 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 (
distreturns an object of class
"dist".The lower triangle of the distance matrix stored by columns in a vector, say
nis the number of observations, i.e.,
n <- attr(do, "Size"), then for $i < j \le n$, 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
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