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
1 
Arguments
x 
numeric matrix or (data frame) or an object of class
"exprSet".
Distances between the rows of

method 
the distance measure to be used. This must be one of

nbproc 
integer, Number of subprocess for parallelization 
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 
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 nonzero 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  sum(x_i y_i) / sqrt [sum(x_i^2) sum(y_i^2)].
abspearson
:Absolute Pearson 1  sum(x_i y_i) / sqrt [sum(x_i^2) sum(y_i^2)] .
correlation
:Also named "Centered Pearson" 1  corr(x,y).
abscorrelation
:Absolute correlation 1   corr(x,y)  with
corr(x,y) = \frac{∑_i x_i y_i \frac1n ∑_i x_i ∑_i% y_i}{% frac: 2nd part √{≤ft(∑_i x_i^2 \frac1n ≤ft( ∑_i x_i \right)^2 % \right)% ≤ft( ∑_i y_i^2 \frac1n ≤ft( ∑_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. ∑_{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.
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*(i1)  i*(i1)/2 + ji]
.
The length of the vector is n*(n1)/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

Note
Multithread (parallelisation) is disable on Windows.
References
Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979) Multivariate Analysis. London: Academic Press.
Wikipedia http://en.wikipedia.org/wiki/Kendall_tau_distance
See Also
daisy
in the ‘cluster’ package with more
possibilities in the case of mixed (contiuous / categorical)
variables.
dist
hcluster
.
Examples
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