ancoord                 package:fpc                 R Documentation

_A_s_y_m_m_e_t_r_i_c _n_e_i_g_h_b_o_r_h_o_o_d _b_a_s_e_d _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 neighborhood based 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 covariance matrix, which is defined by averaging
     the between classes covariance matrices in the neighborhoods of
     the points of the homogeneous class and the projection of the
     covariance matrix within the homogeneous class.

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

     ancoord(xd, clvecd, clnum=1, nn=50, method="mcd", countmode=1000, ...)

_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.

      nn: integer. Number of points which belong to the neighborhood of
          each point (including the point itself).

  method: one of "mve", "mcd" or "classical". Covariance matrix used
          within the homogeneous class. "mcd" and "mve" are robust
          covariance matrices as implemented in 'cov.rob'. "classical"
          refers to the classical covariance matrix.

countmode: optional positive integer. Every 'countmode' algorithm runs
          'ancoord' shows a message.

     ...: no effect

_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"))
       ancf2 <- ancoord(face,grface==4)
       plot(ancf2$proj,col=1+(grface==4))
       # ...done in one step by function plotcluster.

