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:

     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.

_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: Data matrix

 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).

   theta: A set of constraints for each cluster.

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

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

 centers: The final cluster centers.

 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.

    size: The number of data points in each cluster.

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

   error: Returns the value of the error function.

learning: a list with elements

          _n_c_e_n_t_e_r_s The number of the centers,

          _i_n_i_t_c_e_n_t_e_r_s The initial cluster centers, and 

          _i_t_e_r The number of iterations performed.

          _t_h_e_t_a Returns the a priori defined constants.

    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.

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

     `plot.fclust'

_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)
     plot(cl,x)   

