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", nbproc = 2, diag = FALSE, upper = FALSE)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"):
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 form
dist(), the (match.arg()ed) method
argument.
numeric matrix or (data frame) or an object of class
"exprSet".
Distances between the rows of
x will be computed.
the distance measure to be used. This must be one of
"euclidean", "maximum", "manhattan",
"canberra", "binary", "pearson",
"abspearson", "correlation",
"abscorrelation", "spearman" or "kendall".
Any unambiguous substring can be given.
integer, Number of subprocess for parallelization
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.
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:\(\sum_i |x_i - y_i| / |x_i + y_i|\). 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.
pearson:Also named "not centered Pearson" \(1 - \frac{\sum_i x_i y_i}{\sqrt{\sum_i x_i^2 % \sum_i y_i^2}}\).
abspearson:Absolute Pearson \(1 - \left| \frac{\sum_i x_i y_i}{\sqrt{\sum_i x_i^2 % \sum_i y_i^2}} \right| \).
correlation:Also named "Centered Pearson" \(1 - corr(x,y)\).
abscorrelation:Absolute correlation \(1 - | corr(x,y) |\) with
\( corr(x,y) = \frac{\sum_i x_i y_i -\frac1n \sum_i x_i \sum_i% y_i}{% frac: 2nd part \sqrt{\left(\sum_i x_i^2 -\frac1n \left( \sum_i x_i \right)^2 % \right)% \left( \sum_i y_i^2 -\frac1n \left( \sum_i y_i \right)^2 % \right)} }\).
spearman:Compute a distance based on rank. \(\sum(d_i^2)\) where \(d_i\) is the difference in rank between \(x_i\) and \(y_i\).
Dist(x,method="spearman")[i,j] =
cor.test(x[i,],x[j,],method="spearman")$statistic
kendall:Compute a distance based on rank. \(\sum_{i,j} K_{i,j}(x,y)\) with \(K_{i,j}(x,y)\) is 0 if \(x_i, x_j\) in same order as \(y_i,y_j\), 1 if not.
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.
Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979) Multivariate Analysis. London: Academic Press.
Wikipedia https://en.wikipedia.org/wiki/Kendall_tau_distance
x <- matrix(rnorm(100), nrow=5)
Dist(x)
Dist(x, diag = TRUE)
Dist(x, upper = TRUE)
## compute dist with 8 threads
Dist(x,nbproc=8)
Dist(x,method="abscorrelation")
Dist(x,method="kendall")
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