daisy(x, metric = "euclidean", stand = F, type = list())
x
.
Columns of class
numeric
will be recognized as interval scaled variables,
columns of class
factor
will be recognized as nominal variables,
and columns of class
ordered
will be recognized as ordinal variables.
Other variable types should be specified with the
type
argument.
Missing values (NAs) are allowed.
x
are numeric, then this argument
will be ignored.
x
are standardized before
calculating the dissimilarities. Measurements are standardized for each
variable (column), by subtracting the variable's mean value and dividing by
the variable's mean absolute deviation.
If not all columns of
x
are numeric, then this argument
will be ignored.
x
. The list may contain the following components:
ordratio
(ratio scaled variables to be treated as ordinal variables),
logratio
(ratio scaled variables that must be logarithmically transformed),
asymm
(asymmetric binary variables). Each component's value is a vector,
containing the names or the numbers of the corresponding columns of
x
.
Variables not mentioned in the
type
list are interpreted as usual
(see argument
x
).
"dissimilarity"
containing the dissimilarities among
the rows of x. This is typically the input for the functions
pam
,
fanny
,
agnes
or
diana
. See dissimilarity.object for details.
daisy
is fully described in chapter 1 of Kaufman and Rousseeuw (1990).
Compared to
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, asymmetric binary) even when different types occur
in the same dataset.
In the
daisy
algorithm,
missing values in a row of x are not included in the
dissimilarities involving that row. If all variables are interval scaled,
the metric is "euclidean", and ng is the number of columns in which
neither row i and j have NAs, then the dissimilarity d(i,j) returned is
sqrt(ncol(x)/ng) times the Euclidean distance between the two vectors
of length ng shortened to exclude NAs. The rule is similar for the
"manhattan" metric, except that the coefficient is ncol(x)/ng.
If ng is zero, the dissimilarity is NA.
When some variables have a type other than interval scaled, the
dissimilarity between two rows is the weighted sum of the contribution of
each variable.
The weight becomes zero when that variable is missing in either or both
rows, or when the variable is asymmetric binary and both values are
zero. In all other situations, the weight of the variable is 1.
The contribution of nominal or binary variable a to the total dissimilarity
is zero if both values are different, else it
is equal to 1. The contribution of other variables is the absolute
difference of both values, divided by the total range of that variable.
Ordinal variables are first converted to ranks.
If nok is the number of nonzero weights, the dissimilarity is
multiplied by the factor 1/nok and thus ranges between 0 and 1.
If nok is zero, the dissimilarity is NA.
Dissimilarities are used as inputs to cluster analysis and multidimensional scaling. The choice of metric may have a large impact.
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.
x <- matrix(rnorm(10*5, 37), ncol=5) # sample data daisy(x, metric = "manhattan", stand = T) # if all columns are interval scaled variables daisy(x, type = list(logratio = c(2,5))) # if columns 2 and 5 must be logarithmically transformed