clara                package:cluster                R Documentation

_C_l_u_s_t_e_r_i_n_g _L_a_r_g_e _A_p_p_l_i_c_a_t_i_o_n_s

_D_e_s_c_r_i_p_t_i_o_n:

     Computes a `"clara"' object, a list representing a clustering of
     the data into `k' clusters.

_U_s_a_g_e:

     clara(x, k, metric = "euclidean", stand = FALSE, samples = 5,
           sampsize = 40 + 2 * k)

_A_r_g_u_m_e_n_t_s:

       x: data matrix or data frame, each row corresponds to an
          observation, and each column corresponds to a variable.  All
          variables must be numeric. Missing values (NAs) are allowed. 

       k: integer, the number of clusters. It is required that 0 < k <
          n where n is the number of observations (i.e., n =
          `nrow(x)').

  metric: character string specifying the metric to be used for
          calculating dissimilarities between observations. 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. 

   stand: logical, indicating if 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. 

 samples: integer, number of samples to be drawn from the dataset.

sampsize: integer, number of observations in each sample. `sampsize'
          should be higher than the number of clusters (`k') and at
          most the number of observations (n = `nrow(x)').

_D_e_t_a_i_l_s:

     `clara' is fully described in chapter 3 of Kaufman and Rousseeuw
     (1990). Compared to other partitioning methods such as `pam', it
     can deal with much larger datasets.  Internally, this is achieved
     by considering sub-datasets of fixed size (`sampsize') such that
     the time and storage requirements become linear in n rather than
     quadratic.

     Each sub-dataset is partitioned into `k' clusters using the same
     algorithm as in `pam'.
     Once `k' representative objects have been selected from the
     sub-dataset, each observation of the entire dataset is assigned to
     the nearest medoid.

     The sum of the dissimilarities of the observations to their
     closest medoid is used as a measure of the quality of the
     clustering.  The sub-dataset for which the sum is minimal, is
     retained.  A further analysis is carried out on the final
     partition.

     Each sub-dataset is forced to contain the medoids obtained from
     the best sub-dataset until then.  Randomly drawn observations are
     added to this set until `sampsize' has been reached.

_V_a_l_u_e:

     an object of class `"clara"' representing the clustering.  See
     `clara.object' for details.

_N_o_t_e:

     The random sampling is implemented with a very simple scheme (with
     period 2^{16} = 65536) inside the Fortran code, independently of
     R's random number generation, and as a matter of fact,
     deterministically.

     The storage requirement of `clara' computation (for small `k') is
     about O(n * p) + O(j^2) where j = `sampsize', and (n,p) =
     `dim(x)'. The CPU computing time (again neglecting small `k') is
     about O(n * p * j^2 * N), where N = `samples'.

     For ``small'' datasets, the function `pam' can be used directly. 
     What can be considered small, is really a function of available
     computing power, both memory (RAM) and speed. Originally (1990),
     ``small'' meant less than 100 observations; later, the authors
     said ``small (say with fewer than 200 observations)''..

_S_e_e _A_l_s_o:

     `agnes' for background and references; `clara.object', `pam',
     `partition.object', `plot.partition'.

_E_x_a_m_p_l_e_s:

     ## generate 500 objects, divided into 2 clusters.
     x <- rbind(cbind(rnorm(200,0,8), rnorm(200,0,8)),
                cbind(rnorm(300,50,8), rnorm(300,50,8)))
     clarax <- clara(x, 2)
     clarax
     clarax$clusinfo
     plot(clarax)

     ## `xclara' is an artificial data set with 3 clusters of 1000 bivariate
     ## objects each.
     data(xclara)
     ## Plot similar to Figure 5 in Struyf et al (1996)
     plot(clara(xclara, 3), ask = TRUE)

