| dist {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 |
numeric matrix or (data frame). Distances between the rows of
|
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 |
m |
A matrix of distances to be converted to a |
... |
further arguments, passed to the (next) |
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
xandy(supremum norm)manhattan:Absolute distance between the two vectors (1 norm).
canberra:\sum_i |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.
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 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
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*(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 "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 |
methods |
optionally, the distance method used; resulting form
|
References
Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979) Multivariate Analysis. London: Academic Press.
See Also
daisy in the ‘cluster’ package with more
possibilities in the case of mixed (contiuous / categorical)
variables.
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)
## 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