ncoord                  package:fpc                  R Documentation

_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:

     Neighborhood based discriminant coordinates as defined in Hastie
     and Tibshirani (1996) and a robustified version as defined in
     Hennig (2003). The principle is to maximize the projection of a
     between classes covariance matrix, which is defined by averaging
     the between classes covariance matrices in the neighborhoods of
     all points.

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

     ncoord(xd, clvecd, nn=50, weighted=FALSE,
                         sphere="mcd", orderall=TRUE, 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)'.

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

weighted: logical. 'FALSE' corresponds to the original method of Hastie
          and Tibshirani (1996). If 'TRUE', the between classes
          covariance matrices B are weighted by w/trace B, where w is
          some weight depending on the sizes of the classes in the
          neighborhood. Division by trace B reduces the effect of
          outliers. 'TRUE' cooresponds to WNC as defined in Hennig
          (2003).

  sphere: a covariance matrix or one of "mve", "mcd", "classical",
          "none". The matrix used for sphering the data. "mcd" and
          "mve" are robust covariance matrices as implemented in
          'cov.rob'. "classical" refers to the classical covariance
          matrix. "none" means no sphering and use of the raw data.

orderall: logical. By default, the neighborhoods are computed by
          ordering all points each time. If 'FALSE', the neighborhoods
          are computed by selecting 'nn' times the nearest point from
          the remaining points, which may be faster sometimes.

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

     ...: no effect

_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:

     Hastie, T. and Tibshirani, R.  (1996). Discriminant adaptive
     nearest neighbor classification. _IEEE Transactions on Pattern
     Analysis and Machine Intelligence_ 18, 607-616. 

     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"))
       ncf <- ncoord(face,grface)
       plot(ncf$proj,col=grface)
       ncf2 <- ncoord(face,grface,weighted=TRUE)
       plot(ncf2$proj,col=grface)
       # ...done in one step by function plotcluster.

