daisy {cluster}R Documentation

Dissimilarity Matrix Calculation

Description

Compute all the pairwise dissimilarities (distances) between observations in the data set. The original variables may be of mixed types.

Usage

daisy(x, metric = c("euclidean", "manhattan", "gower"),
      stand = FALSE, type = list())

Arguments

x numeric matrix or data frame. Dissimilarities will be computed between the rows of x. Columns of mode numeric (i.e. all columns when x is a matrix) 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.
metric character string specifying the metric to be used. The currently available options are "euclidean" (the default), "manhattan" and "gower".
Euclidean distances are root sum-of-squares of differences, and manhattan distances are the sum of absolute differences.
“Gower's distance” is chosen by metric "gower" or automatically if some columns of x are not numeric. Also known as Gower's coefficient (1971), expressed as a dissimilarity, this implies that a particular standardisation will be applied to each variable, and the “distance” between two units is the sum of all the variable-specific distances, see the details section.
stand logical flag: if TRUE, then the measurements in 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, stand will be ignored and Gower's standardization (based on the range) will be applied in any case, see argument metric, above, and the details section.
type list for specifying some (or all) of the types of the variables (columns) in 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) and "symm" (symmetric 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).

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, (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 (1971). If x contains any columns of these data-types, both arguments metric and 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.

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 efficiently.

Note that daisy now gives a warning when 2-valued numerical variables don't have an explicit type specified, because the reference authors recommend to consider using "asymm".

In the daisy algorithm, missing values in a row of x are not included in the dissimilarities involving that row. There are two main cases,

  1. 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.
  2. When some variables have a type other than interval scaled, the dissimilarity between two rows is the weighted sum of the contributions 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 a nominal or binary variable to the total dissimilarity is 0 if both values are different, 1 otherwise. 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 = 0, the dissimilarity is set to NA.

Value

an object of class "dissimilarity" containing the dissimilarities among the rows of x. This is typically the input for the functions pam, fanny, agnes or diana. For more details, see dissimilarity.object.

Background

Dissimilarities are used as inputs to cluster analysis and multidimensional scaling. The choice of metric may have a large impact.

References

Gower, J. C. (1971) A general coefficient of similarity and some of its properties, Biometrics 27, 623–637.

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.

See Also

dissimilarity.object, dist, pam, fanny, clara, agnes, diana.

Examples

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)))
[Package cluster version 1.11.5 Index]