Description Usage Arguments Details Value Examples
Calculates distance matrices in parallel using multiple threads. Supports 41 predefined distance measures and userdefined distance functions.
1 2 
x 
a numeric matrix (each row is one series) or list of numeric matrices for multidimensional series (each matrix is one series, a row is a dimension of a series) 
method 
the distance measure to be used. A list of all available distance methods can be found in the details section below. 
diag 
logical value indicating whether the diagonal of the distance matrix should be printed by print.dist. 
upper 
logical value indicating whether the upper triangle of the distance matrix should be printed by print.dist 
threads 
number of cpu threads for calculating a distance matrix. Default is the maximum amount of cpu threads available on the system. 
... 
additional parameters which will be passed to the distance methods. See details section below. 
custom
Defining and compiling a userdefined C++ distance function, as well as creating an external pointer to the function can easily be achieved with the cppXPtr
function of the RcppXPtrUtils package. The resulting Xptr
external pointer object needs to be passed to parDist
using the func
parameter.
Parameters:
func
(Xptr)External pointer to a userdefined distance function with the following signature:
double customDist(const arma::mat &A, const arma::mat &B)
Note that the return value must be a double
and the two parameters must be of type const arma::mat ¶m
.
More information about the Armadillo library can be found at http://arma.sourceforge.net/docs.html or as part of the documentation of the RcppArmadillo package.
An exemplary definition and usage of an userdefined euclidean distance function can be found in the examples section below.
Distance methods for continuous input variables
bhjattacharyya
The Bhjattacharyya distance.
Type: continuous
Formula: sqrt(sum_i (sqrt(x_i)  sqrt(y_i))^2)).
Details: See pr_DB$get_entry("bhjattacharyya")
in proxy.
bray
The Bray/Curtis dissimilarity.
Type: continuous
Formula: sum_i x_i  y_i / sum_i (x_i + y_i).
Details: See pr_DB$get_entry("bray")
in proxy.
canberra
The Canberra distance (with compensation for excluded components). Terms with zero numerator and denominator are omitted from the sum and treated as if the values were missing.
Type: continuous
Formula: sum_i x_i  y_i / x_i + y_i.
Details: See pr_DB$get_entry("canberra")
in proxy.
chord
The Chord distance.
Type: continuous
Formula: sqrt(2 * (1  xy / sqrt(xx * yy))).
Details: See pr_DB$get_entry("chord")
in proxy.
divergence
The Divergence distance.
Type: continuous
Formula: sum_i (x_i  y_i)^2 / (x_i + y_i)^2.
Details: See pr_DB$get_entry("divergence")
in proxy.
dtw
Implementation of a multidimensional Dynamic Time Warping algorithm.
Type: continuous
Formula: Euclidean distance sqrt(sum_i (x_i  y_i)^2).
Parameters:
window.size
(integer, optional)Size of the window of the SakoeChiba band. If the absolute length difference of two series x and y is larger than the window.size, the window.size is set to the length difference.
norm.method
(character, optional)Normalization method for DTW distances.
path.length
Normalization with the length of the warping path.
n
Normalization with n. n is the length of series x.
n+m
Normalization with n + m. n is the length of series x, m is the length of series y.
step.pattern
(character or stepPattern of dtw package, default: symmetric1
)The following step patterns of the dtw package are supported:
asymmetric
(Normalization hint: n)
asymmetricP0
(Normalization hint: n)
asymmetricP05
(Normalization hint: n)
asymmetricP1
(Normalization hint: n)
asymmetricP2
(Normalization hint: n)
symmetric1
(Normalization hint: path.length)
symmetric2
or symmetricP0
(Normalization hint: n+m)
symmetricP05
(Normalization hint: n+m)
symmetricP1
(Normalization hint: n+m)
symmetricP2
(Normalization hint: n+m)
For a detailed description see stepPattern
of the dtw package.
euclidean
The Euclidean distance/L_2norm (with compensation for excluded components).
Type: continuous
Formula: sqrt(sum_i (x_i  y_i)^2)).
Details: See pr_DB$get_entry("euclidean")
in proxy.
fJaccard
The fuzzy Jaccard distance.
Type: binary
Formula: sum_i (min{x_i, y_i}) / sum_i(max{x_i, y_i}).
Details: See pr_DB$get_entry("fJaccard")
in proxy.
geodesic
The geoedesic distance, i.e. the angle between x and y.
Type: continuous
Formula: arccos(xy / sqrt(xx * yy)).
Details: See pr_DB$get_entry("geodesic")
in proxy.
hellinger
The Hellinger distance.
Type: continuous
Formula: sqrt(sum_i (sqrt(x_i / sum_i x)  sqrt(y_i / sum_i y)) ^ 2).
Details: See pr_DB$get_entry("hellinger")
in proxy.
kullback
The KullbackLeibler distance.
Type: continuous
Formula: sum_i [x_i * log((x_i / sum_j x_j) / (y_i / sum_j y_j)) / sum_j x_j)].
Details: See pr_DB$get_entry("kullback")
in proxy.
mahalanobis
The Mahalanobis distance. The VarianceCovarianceMatrix is estimated from the input data if unspecified.
Type: continuous
Formula: sqrt((x  y) Sigma^(1) (x  y)).
Parameters:
cov
(numeric matrix, optional)The covariance matrix (p x p) of the distribution.
inverted
(logical, optional)If TRUE, cov is supposed to contain the inverse of the covariance matrix.
Details: See pr_DB$get_entry("mahalanobis")
in proxy or mahalanobis
in stats.
manhattan
The Manhattan/CityBlock/Taxi/L_1norm distance (with compensation for excluded components).
Type: continuous
Formula: sum_i x_i  y_i.
Details: See pr_DB$get_entry("manhattan")
in proxy.
maximum
The Maximum/Supremum/Chebyshev distance.
Type: continuous
Formula: max_i x_i  y_i.
Details: See pr_DB$get_entry("maximum")
in proxy.
minkowski
The Minkowski distance/pnorm (with compensation for excluded components).
Type: continuous
Formula: (sum_i (x_i  y_i)^p)^(1/p).
Parameters:
p
(double, optional)The pth root of the sum of the pth powers of the differences of the components.
Details: See pr_DB$get_entry("minkowski")
in proxy.
podani
The Podany measure of discordance is defined on ranks with ties. In the formula, for two given objects x and y, n is the number of variables, a is is the number of pairs of variables ordered identically, b the number of pairs reversely ordered, c the number of pairs tied in both x and y (corresponding to either joint presence or absence), and d the number of all pairs of variables tied at least for one of the objects compared such that one, two, or thee scores are zero.
Type: continuous
Formula: 1  2 * (a  b + c  d) / (n * (n  1)).
Details: See pr_DB$get_entry("podani")
in proxy.
soergel
The Soergel distance.
Type: continuous
Formula: sum_i x_i  y_i / sum_i max{x_i, y_i}.
Details: See pr_DB$get_entry("soergel")
in proxy.
wave
The Wave/Hedges distance.
Type: continuous
Formula: sum_i (1  min(x_i, y_i) / max(x_i, y_i)).
Details: See pr_DB$get_entry("wave")
in proxy.
whittaker
The Whittaker distance.
Type: continuous
Formula: sum_i x_i / sum_i x  y_i / sum_i y / 2.
Details: See pr_DB$get_entry("whittaker")
in proxy.
Distance methods for binary input variables
Notation:
a: number of (TRUE, TRUE) pairs
b: number of (FALSE, TRUE) pairs
c: number of (TRUE, FALSE) pairs
d: number of (FALSE, FALSE) pairs
Note: Similarities are converted to distances.
binary
The Jaccard Similarity for binary data. It is the proportion of (TRUE, TRUE) pairs, but not considering (FALSE, FALSE) pairs.
Type: binary
Formula: a / (a + b + c).
Details: See pr_DB$get_entry("binary")
in proxy.
braunblanquet
The BraunBlanquet similarity.
Type: binary
Formula: a / max{(a + b), (a + c)}.
Details: See pr_DB$get_entry("braunblanquet")
in proxy.
cosine
The cosine similarity.
Type: continuous
Formula: (a * b) / (a*b).
Details: See pr_DB$get_entry("cosine")
in proxy.
dice
The Dice similarity.
Type: binary
Formula: 2a / (2a + b + c).
Details: See pr_DB$get_entry("dice")
in proxy.
fager
The Fager / McGowan distance.
Type: binary
Formula: a / sqrt((a + b)(a + c))  sqrt(a + c) / 2.
Details: See pr_DB$get_entry("fager")
in proxy.
faith
The Faith similarity.
Type: binary
Formula: (a + d/2) / n.
Details: See pr_DB$get_entry("faith")
in proxy.
hamman
The Hamman Matching similarity for binary data. It is the proportion difference of the concordant and discordant pairs.
Type: binary
Formula: ([a + d]  [b + c]) / n.
Details: See pr_DB$get_entry("hamman")
in proxy.
hamming
The hamming distance between two vectors A and B is the fraction of positions where there is a mismatch.
Formula: \textit{\# of }(A != B) / \textit{\# in A (or B)}
kulczynski1
Kulczynski similarity for binary data. Relates the (TRUE, TRUE) pairs to discordant pairs.
Type: binary
Formula: a / (b + c).
Details: See pr_DB$get_entry("kulczynski1")
in proxy.
kulczynski2
Kulczynski similarity for binary data. Relates the (TRUE, TRUE) pairs to the discordant pairs.
Type: binary
Formula: [a / (a + b) + a / (a + c)] / 2.
Details: See pr_DB$get_entry("kulczynski2")
in proxy.
michael
The Michael similarity.
Type: binary
Formula: 4(ad  bc) / [(a + d)^2 + (b + c)^2].
Details: See pr_DB$get_entry("michael")
in proxy.
mountford
The Mountford similarity for binary data.
Type: binary
Formula: 2a / (ab + ac + 2bc).
Details: See pr_DB$get_entry("mountford")
in proxy.
mozley
The Mozley/Margalef similarity.
Type: binary
Formula: an / (a + b)(a + c).
Details: See pr_DB$get_entry("mozley")
in proxy.
ochiai
The Ochiai similarity.
Type: binary
Formula: a / sqrt[(a + b)(a + c)].
Details: See pr_DB$get_entry("ochiai")
in proxy.
phi
The Phi similarity (= ProductMomentCorrelation for binary variables).
Type: binary
Formula: (ad  bc) / sqrt[(a + b)(c + d)(a + c)(b + d)].
Details: See pr_DB$get_entry("phi")
in proxy.
russel
The Russel/Raosimilarity for binary data. It is just the proportion of (TRUE, TRUE) pairs.
Type: binary
Formula: a / n.
Details: See pr_DB$get_entry("russel")
in proxy.
simple matching
The Simple Matching similarity for binary data. It is the proportion of concordant pairs.
Type: binary
Formula: (a + d) / n.
Details: See pr_DB$get_entry("simple matching")
in proxy.
simpson
The Simpson similarity.
Type: binary
Formula: a / min{(a + b), (a + c)}.
Details: See pr_DB$get_entry("simpson")
in proxy.
stiles
The Stiles similarity. Identical to the logarithm of Krylov's distance.
Type: binary
Formula: log(n(adbc  0.5n)^2 / [(a + b)(c + d)(a + c)(b + d)]).
Details: See pr_DB$get_entry("stiles")
in proxy.
tanimoto
The Rogers/Tanimoto similarity for binary data. Similar to the simple matching coefficient, but putting double weight on the discordant pairs.
Type: binary
Formula: (a + d) / (a + 2b + 2c + d).
Details: See pr_DB$get_entry("tanimoto")
in proxy.
yule
The Yule similarity.
Type: binary
Formula: (ad  bc) / (ad + bc).
Details: See pr_DB$get_entry("yule")
in proxy.
yule2
The Yule similarity.
Type: binary
Formula: (sqrt(ad)  sqrt(bc)) / (sqrt(ad) + sqrt(bc)).
Details: See pr_DB$get_entry("yule2")
in proxy.
parDist
returns 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 
method 
optionally, the distance method used; resulting from

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42  ## Not run:
## predefined distance functions
# defining a matrix, where each row corresponds to one series
sample.matrix < matrix(c(1:100), ncol = 10)
# euclidean distance
parDist(x = sample.matrix, method = "euclidean")
# minkowski distance with parameter p=2
parDist(x = sample.matrix, method = "minkowski", p=2)
# dynamic time warping distance
parDist(x = sample.matrix, method = "dtw")
# dynamic time warping distance normalized with warping path length
parDist(x = sample.matrix, method = "dtw", norm.method="path.length")
# dynamic time warping with different step pattern
parDist(x = sample.matrix, method = "dtw", step.pattern="symmetric2")
# dynamic time warping with window size constraint
parDist(x = sample.matrix, method = "dtw", step.pattern="symmetric2", window.size=1)
## multidimensional distance functions using list of matrices
# defining a list of matrices, where each list entry row corresponds to a two dimensional series
tmp.mat < matrix(c(1:40), ncol = 10)
sample.matrix.list < list(tmp.mat[1:2,], tmp.mat[3:4,])
# multidimensional euclidean distance
parDist(x = sample.matrix.list, method = "euclidean")
# multidimensional dynamic time warping
parDist(x = sample.matrix.list, method = "dtw")
## userdefined distance function
library(RcppArmadillo)
# Use RcppXPtrUtils for simple usage of C++ external pointers
library(RcppXPtrUtils)
# compile userdefined function and return pointer (RcppArmadillo is used as dependency)
euclideanFuncPtr < cppXPtr(
"double customDist(const arma::mat &A, const arma::mat &B) {
return sqrt(arma::accu(arma::square(A  B)));
}", depends = c("RcppArmadillo"))
# distance matrix for userdefined euclidean distance function (note that method is set to "custom")
parDist(matrix(1:16, ncol=2), method="custom", func = euclideanFuncPtr)
## End(Not run)

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