partcoef                package:Mfuzz                R Documentation

_C_a_l_c_u_l_a_t_i_o_n _o_f _t_h_e _p_a_r_t_i_t_i_o_n _c_o_e_f_f_i_c_i_e_n_t _m_a_t_r_i_x _f_o_r _s_o_f_t _c_l_u_s_t_e_r_i_n_g

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

     This function calculates partition coefficient for clusters within
     a range of cluster parameters. It can be used to determine the
     parameters which lead to uniform clustering.

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

     partcoef(eset,crange=seq(4,32,4),mrange=seq(1.05,2,0.1),...)

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

    eset: object of class ExpressionSet.

  crange: range of number of clusters 'c'.

  mrange: range of clustering paramter 'm'.

     ...: additional arguments for underlying 'mfuzz'.

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

     Introduced by Bezdek (1981), the partition coefficient F is
     defined as the sum of squares of values of the partition matrix
     divided by the number of values. It is maximal if the partition is
     hard and reaches a minimum for U=1/c  when every gene is equally
     assigned to every cluster.

     It is well-known that the partition coefficient tends to decrease
     monotonically with increasing n. To reduce this tendency we
     defined a normalized partition coefficient where the partition for
     uniform partitions are subtracted from the actual partition
     coefficients (Futschik and Kasabov,2002).

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

     The function generates the matrix of partition coefficients  for a
     range of 'c' and 'm' values. It also produces a matrix of
     normalised partition coefficients  as well as a matrix with
     partition coefficient for uniform partitions.

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

     Matthias E. Futschik (<URL:
     http://itb.biologie.hu-berlin.de/~futschik>)

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


        1.  J.C.Bezdek, Pattern recognition with fuzzy objective
           function algorithms, Plenum, 1981

        2.  M.E. Futschik and N.K. Kasabov. Fuzzy clustering of gene
           expression data, Proceedings of World Congress of
           Computational Intelligence WCCI 2002, Hawaii, IEEE Press,
           2002

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

     if (interactive()){
     data(yeast)
     # Data pre-processing
     yeastF <- filter.NA(yeast)
     yeastF <- fill.NA(yeastF)
     yeastF <- standardise(yeastF)

     #### parameter selection
     yeastFR <- randomise(yeastF)
     cl <- mfuzz(yeastFR,c=20,m=1.1)
     mfuzz.plot(yeastFR,cl=cl,mfrow=c(4,5)) # shows cluster structures (non-uniform partition)

      tmp  <- partcoef(yeastFR) # This might take some time.
      F <- tmp[[1]];F.n <- tmp[[2]];F.min <- tmp[[3]]

      # Which clustering parameters result in a uniform partition?  
      F > 1.01 * F.min

     cl <- mfuzz(yeastFR,c=20,m=1.25) # produces uniform partion 

     mfuzz.plot(yeastFR,cl=cl,mfrow=c(4,5))
     # uniform coloring of temporal profiles indicates uniform partition
     }

