cmahal                  package:fpc                  R Documentation

_G_e_n_e_r_a_t_i_o_n _o_f _t_u_n_i_n_g _c_o_n_s_t_a_n_t _f_o_r _M_a_h_a_l_a_n_o_b_i_s _f_i_x_e_d _p_o_i_n_t _c_l_u_s_t_e_r_s.

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

     Generates tuning constants 'ca' for 'fixmahal' dependent on the
     number of points and variables of the current fixed point cluster
     (FPC).

     This is experimental and only thought for use in 'fixmahal'.

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

     cmahal(n, p, nmin, cmin, nc1, c1 = cmin, q = 1)

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

       n: positive integer. Number of points.

       p: positive integer. Number of variables.

    nmin: integer larger than 1. Smallest number of points for which
          'ca' is computed. For smaller FPC sizes, 'ca' is set to the
          value for 'nmin'.

    cmin: positive number. Minimum value for 'ca'.

     nc1: positive integer. Number of points at which 'ca=c1'.

      c1: positive numeric. Tuning constant for 'cmahal'. Value for
          'ca' for FPC size equal to 'nc1'.

       q: numeric between 0 and 1. 1 for steepest possible descent of
          'ca' as function of the FPC size. Should presumably always be
          1.

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

     Some experiments suggest that the tuning constant 'ca' should
     decrease with increasing FPC size and increase with increasing 'p'
     in 'fixmahal'. This is to prevent too small meaningless FPCs while
     maintaining the significant larger ones. 'cmahal' with 'q=1'
     computes 'ca' in such a way that as long as 'ca>cmin', the
     decrease in 'n' is as steep as possible in order to maintain the
     validity of the convergence theorem in Hennig and Christlieb
     (2002).

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

     A numeric vector of length 'n', giving the values for 'ca' for all
     FPC sizes smaller or equal to 'n'.

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

     Christian Hennig chrish@stats.ucl.ac.uk <URL:
     http://www.homepages.ucl.ac.uk/~ucakche/>

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

     Hennig, C. and Christlieb, N. (2002) Validating visual clusters in
     large datasets: Fixed point clusters of spectral features,
     _Computational Statistics and Data Analysis_ 40, 723-739.

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

     'fixmahal'

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

       plot(1:100,cmahal(100,3,nmin=5,cmin=qchisq(0.99,3),nc1=90),
            xlab="FPC size", ylab="cmahal")

