daisy                package: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 ('NA's) 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)))

