fuzziness                package:clue                R Documentation

_P_a_r_t_i_t_i_o_n _F_u_z_z_i_n_e_s_s

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

     Compute the fuzziness of partitions.

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

     cl_fuzziness(x, method = NULL, normalize = TRUE)

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

       x: a cluster ensemble of partitions, or an R object coercible to
          such.

  method: a character string indicating the fuzziness measure to be
          employed, or 'NULL' (default), or a function to be taken as a
          user-defined method.  Currently available built-in methods
          are '"PC"' (Partition Coefficient) and '"PE"' (Partition
          Entropy), with the default corresponding to the first one. 
          If 'method' is a character string, its lower-cased version is
          matched against the lower-cased names of the available
          built-in methods using 'pmatch'.

normalize: a logical indicating whether the fuzziness measure should be
          normalized in a way that hard partitions have value 0, and
          "completely fuzzy" partitions (where for all objects, all
          classes get the same membership) have value 1.

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

     If m contains the membership values of a partition, the
     (unnormalized) Partition Coefficient and Partition Entropy are
     given by sum_{n,i} m_{n,i}^2 and sum_{n,i} H(m_{n,i}),
     respectively, where u log(u) - (1-u) log(1-u).

     Note that the normalization used here is different from the
     normalizations typically found in the literature.

     If a user-defined fuzziness method is to be employed, is must be a
     function taking a matrix of membership values and a logical to
     indicate whether normalization is to be performed as its arguments
     (in that order; argument names are not used).

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

     An object of class '"cl_fuzziness"' giving the fuzziness values.

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

     J. C. Bezdek (1981). _Pattern Recognition with Fuzzy Objective
     Function Algorithms_. New York: Plenum.

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

     Function 'fclustIndex' in package 'e1071', which also computes
     several other "fuzzy cluster indexes" (typically based on more
     information than just the membership values).

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

     if(require("e1071", quiet = TRUE)) {
         ## Use an on-line version of fuzzy c-means from package e1071 if
         ## available.
         data("Cassini")
         pens <- cl_boot(Cassini$x, B = 15, k = 3, algorithm = "cmeans",
                         parameters = list(method = "ufcl"))
         pens
         summary(cl_fuzziness(pens, "PC"))
         summary(cl_fuzziness(pens, "PE"))
     }

