dist                   package:mva                   R Documentation

Distance Matrix Computation

Description:

     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.

Usage:

     dist(x, method = "euclidean", diag = FALSE, upper = FALSE)

     print.dist(x, diag = NULL, upper = NULL, ...)
     as.matrix.dist(x)
     as.dist(m, diag = FALSE, upper = FALSE)

Arguments:

       x: A matrix or (data frame).  Distances between the rows of `x'
          will be computed.

  method: The distance measure to be used. This must be one of
          `"euclidean"', `"maximum"', `"manhattan"', `"canberra"' or
          `"binary"'. Any unambiguous substring can be given.

    diag: A logical value indicating whether the diagonal of the
          distance matrix should be printed by `print.dist'.

   upper: A logical value indicating whether the upper triangle of the
          distance matrix should be printed by `print.dist'.

       m: A matrix of distances to be converted to a `"dist"' object
          (only the lower triangle is used, the rest is ignored).

     ...: further arguments, passed to the (next) `print' method.

Details:

     Available distance measures are (written for two vectors x and y):

     `euclidean': Usual square distance between the two vectors (2
          norm).

     `maximum': Maximum distance between two components of x and y
          (supremum norm)

     `manhattan': Absolute distance between the two vectors (1 norm).

     `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.


     `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.

     Missing values are allowed, and are excluded from all computations
     involving the rows within which they occur.  If some columns are
     excluded in calculating a Euclidean, Manhattan or Canberra
     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 functions `as.matrix.dist()' and `as.dist()' can be used for
     conversion between objects of class `"dist"' and conventional
     distance matrices and vice versa.

Value:

     An object of class `"dist"'.

     The lower triangle of the distance matrix stored by columns in a
     single vector.  The vector has the attributes `"Size"', `"Diag"',
     `"Upper"', `"Labels"' and `"class"' equal to `"dist"'.

References:

     Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979) Multivariate
     Analysis. London: Academic Press.

See Also:

     `hclust'.

Examples:

     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))
     names(d) <- LETTERS[1:5]
     print(d, digits = 3)

     ## 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)

