scaclust                package:e1071                R Documentation

_F_u_z_z_y _C_l_u_s_t_e_r_i_n_g _u_s_i_n_g _S_c_a_t_t_e_r _M_a_t_r_i_c_e_s

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

     Four fuzzy clustering methods, namely the Adaptive distances
     method, the Minimum total volume method, the Sum of all normalized
     determinants and the the Maximum likelihood method (Product of
     Determinants) that are based on the calculation of the scatter
     matrices.

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

     scaclust(x, centers, iter.max=100, verbose=FALSE, method="ad",
              theta = NULL)

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

       x: The data matrix, where the columns correspond to the
          variables and the rows to the observations.

 centers: Number of clusters or initial values for cluster centers

iter.max: Maximum number of iterations

 verbose: If `TRUE', make some output during learning

  method: If `"ad"', then we have the Adaptive distances method, if
          `"mtv"' the Minimum total volume method, if `"sand"' the Sum
          of all normalized determinants method and if `"mlm"' the
          Maximum likelihood method (Product of Determinants).
          Abbreviations of the method names are also accepted.

   theta: A set of constraints for each cluster

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

     The data given by `x' is clustered by 4 fuzzy algorithms based on
     the scatter matrices computation.

     If `centers' is a matrix, its rows are taken as the initial
     cluster centers. If `centers' is an integer, `centers' rows of `x'
     are randomly chosen as initial values.

     The algorithm stops when the maximum number of iterations (given
     by `iter.max') is reached.

     If `verbose' is `TRUE', it displays for each iteration the number
     the value of the objective function.

     If `method' is `"ad"', then we have the Adaptive distances method,
     if `"mtv"' the Minimum total volume method, if `"sand"' the Sum of
     all normalized determinants method and if `"mlm"' the Maximum
     likelihood method (Product of Determinants). Note that all these
     algorithms are adapted for a fuzzification parameter of a value 2.

     `theta' is by default 1.0 for every cluster. The relative volumes
     of the clusters are constrained a priori by these constants. An
     inappropriate choice can lead to a bad clustering. The Maximum
     likelihood method does not need this parameter.

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

     `scaclust' returns an object of class `"fclust"'. 

 centers: The final cluster centers.

    size: The number of data points in each cluster.

 cluster: Vector containing the indices of the clusters where the data
          points are assigned to. The maximum membership value of a
          point is considered for partitioning it to a cluster.

    iter: The number of iterations performed.

membership: a matrix with the membership values of the data points to
          the clusters.

withinerror: Returns the value of the error function.

    call: Returns a call in which all of the arguments are specified by
          their names.

_A_u_t_h_o_r(_s):

     Evgenia Dimitriadou

_R_e_f_e_r_e_n_c_e_s:

     P. J. Rousseeuw, L. Kaufman, and E. Trauwaert. Fuzzy Clustering
     using Scatter Matrices. Computational Statistics & Data Analysis,
     vol.23, p.135-151, 1996.

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

     ## a 2-dimensional example
     x<-rbind(matrix(rnorm(100,sd=0.3),ncol=2),
              matrix(rnorm(100,mean=1,sd=0.3),ncol=2))
     cl<-scaclust(x,2,20,verbose=TRUE,method="ad")
     print(cl)

