cluster (version 1.2-1)

daisy: Dissimilarity Matrix Calculation

Description

Returns a matrix containing all the pairwise dissimilarities (distances) between observations in the dataset. The original variables may be of mixed types.

Usage

daisy(x, metric = "euclidean", stand = F, type = list())

Arguments

x

data matrix or dataframe. Dissimilarities will be computed between the rows of x. Columns of class numeric will be recognized as interval scaled variables, columns of class factor will be recognized as nominal variab

metric

character string specifying the metric to be used. The currently available options are "euclidean" and "manhattan". Euclidean distances are root sum-of-squares of differences, and manhattan distances are the sum of absolute differences. If not all columns

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

type

list containing 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

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. See dissimilarity.object for details.

BACKGROUND

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

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.

References

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
## Compute the dissimilarities using Euclidean metric and without
## standardization 
daisy(agriculture, metric = "euclidean", stand = FALSE)

data(flower)
## Example 2 in ref
daisy(flower, type = list(asymm = 3))
daisy(flower, type = list(asymm = c(1, 3), ordratio = 7))