adcoord                 package:fpc                 R Documentation

_A_s_y_m_m_e_t_r_i_c _d_i_s_c_r_i_m_i_n_a_n_t _c_o_o_r_d_i_n_a_t_e_s

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

     Asymmetric discriminant coordinates as defined in Hennig (2003).
     Asymmetric discriminant projection means that there are two
     classes, one of which is treated as the homogeneous class (i.e.,
     it should appear homogeneous and separated in the resulting
     projection) while the other may be heterogeneous.  The principle
     is to maximize the ratio between the projection of a between
     classes separation matrix and the projection of the covariance
     matrix within the homogeneous class.

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

     adcoord(xd, clvecd, clnum=1)

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

      xd: the data matrix; a numerical object which can be coerced to a
          matrix.

  clvecd: integer vector of class numbers; length must equal
          'nrow(xd)'.

   clnum: integer. Number of the homogeneous class.

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

     The square root of the homogeneous classes covariance matrix is
     inverted by use of 'tdecomp', which can be expected to give
     reasonable results for singular within-class covariance matrices.

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

     List with the following components 

      ev: eigenvalues in descending order.

   units: columns are coordinates of projection basis vectors. New
          points 'x' can be projected onto the projection basis vectors
          by 'x %*% units'

    proj: projections of 'xd' onto 'units'.

_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. (2003) Symmetric, asymmetric, and robust linear
     dimension reduction for classification, submitted, <URL:
     http://stat.ethz.ch/Research-Reports/108.html>.

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

     'plotcluster' for straight forward discriminant plots. 'discrproj'
     for alternatives. 'rFace' for generation of the example data used
     below.

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

       set.seed(4634)
       face <- rFace(600,dMoNo=2,dNoEy=0)
       grface <- as.integer(attr(face,"grouping"))
       adcf <- adcoord(face,grface==2)
       adcf2 <- adcoord(face,grface==4)
       plot(adcf$proj,col=1+(grface==2))
       plot(adcf2$proj,col=1+(grface==4))
       # ...done in one step by function plotcluster.

