Compute all the pairwise dissimilarities (distances) between observations
in the data set. The original variables may be of mixed types. In
that case, or whenever
metric = "gower" is set, a
generalization of Gower's formula is used, see ‘Details’
daisy(x, metric = c("euclidean", "manhattan", "gower"), stand = FALSE, type = list(), weights = rep.int(1, p), warnBin = warnType, warnAsym = warnType, warnConst = warnType, warnType = TRUE)
numeric matrix or data frame, of dimension n x p,
say. Dissimilarities will be computed
between the rows of
character string specifying the metric to be used.
The currently available options are
“Gower's distance” is chosen by metric
logical flag: if TRUE, then the measurements in
If not all columns of
list for specifying some (or all) of the types of the
variables (columns) in
Each component is a (character or numeric) vector, containing either
the names or the numbers of the corresponding columns of
Variables not mentioned in
an optional numeric vector of length p(=
logicals indicating if the corresponding type checking warnings should be signalled (when found).
logical indicating if all the type checking warnings should be active or not.
The original version of
daisy is fully described in chapter 1
of Kaufman and Rousseeuw (1990).
dist whose input must be numeric
variables, the main feature of
daisy is its ability to handle
other variable types as well (e.g. nominal, ordinal, (a)symmetric
binary) even when different types occur in the same data set.
The handling of nominal, ordinal, and (a)symmetric binary data is
achieved by using the general dissimilarity coefficient of Gower
x contains any columns of these
data-types, both arguments
stand will be
ignored and Gower's coefficient will be used as the metric. This can
also be activated for purely numeric data by
metric = "gower".
With that, each variable (column) is first standardized by dividing
each entry by the range of the corresponding variable, after
subtracting the minimum value; consequently the rescaled variable has
range [0,1], exactly.
Note that setting the type to
symm (symmetric binary) gives the
same dissimilarities as using nominal (which is chosen for
non-ordered factors) only when no missing values are present, and more
daisy signals a warning when 2-valued numerical
variables do not have an explicit
type specified, because the
reference authors recommend to consider using
warning may be silenced by
warnBin = FALSE.
daisy algorithm, missing values in a row of x are not
included in the dissimilarities involving that row. There are two
If all variables are interval scaled (and
"gower"), the metric is "euclidean", and
n_g is the number of columns in which
neither row i and j have NAs, then the dissimilarity d(i,j) returned is
sqrt(p/n_g) (p=ncol(x)) times the
Euclidean distance between the two vectors of length n_g
shortened to exclude NAs. The rule is similar for the "manhattan"
metric, except that the coefficient is p/n_g. If n_g = 0,
the dissimilarity is NA.
When some variables have a type other than interval scaled, or
metric = "gower" is specified, the
dissimilarity between two rows is the weighted mean of the contributions of
each variable. Specifically,
d_ij = d(i,j) = sum(k=1:p; w_k delta(ij;k) d(ij,k)) / sum(k=1:p; w_k delta(ij;k)).
In other words, d_ij is a weighted mean of
d(ij,k) with weights w_k delta(ij;k),
delta(ij;k) is 0 or 1, and
d(ij,k), the k-th variable contribution to the
total distance, is a distance between
The 0-1 weight delta(ij;k) becomes zero
when the variable
x[,k] is missing in either or both rows
(i and j), or when the variable is asymmetric binary and both
values are zero. In all other situations it is 1.
The contribution d(ij,k) of a nominal or binary variable to the total
dissimilarity is 0 if both values are equal, 1 otherwise.
The contribution of other variables is the absolute difference of
both values, divided by the total range of that variable. Note
that “standard scoring” is applied to ordinal variables,
i.e., they are replaced by their integer codes
that this is not the same as using their ranks (since there
typically are ties).
As the individual contributions d(ij,k) are in
[0,1], the dissimilarity d_ij will remain in
If all weights w_k delta(ij;k) are zero,
the dissimilarity is set to
an object of class
"dissimilarity" containing the
dissimilarities among the rows of
x. This is typically the
input for the functions
diana. For more details, see
Dissimilarities are used as inputs to cluster analysis and multidimensional scaling. The choice of metric may have a large impact.
Anja Struyf, Mia Hubert, and Peter and Rousseeuw, for the original
Martin Maechler improved the
NA handling and
type specification checking, and extended functionality to
metric = "gower" and the optional
Gower, J. C. (1971) A general coefficient of similarity and some of its properties, Biometrics 27, 857–874.
Kaufman, L. and Rousseeuw, P.J. (1990) Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York.
Struyf, A., Hubert, M. and Rousseeuw, P.J. (1997) Integrating Robust Clustering Techniques in S-PLUS, Computational Statistics and Data Analysis 26, 17–37.
data(agriculture) ## Example 1 in ref: ## Dissimilarities using Euclidean metric and without standardization d.agr <- daisy(agriculture, metric = "euclidean", stand = FALSE) d.agr as.matrix(d.agr)[,"DK"] # via as.matrix.dist(.) ## compare with as.matrix(daisy(agriculture, metric = "gower")) data(flower) ## Example 2 in ref summary(dfl1 <- daisy(flower, type = list(asymm = 3))) summary(dfl2 <- daisy(flower, type = list(asymm = c(1, 3), ordratio = 7))) ## this failed earlier: summary(dfl3 <- daisy(flower, type = list(asymm = c("V1", "V3"), symm= 2, ordratio= 7, logratio= 8)))
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