

sammon(MASS)                                 R Documentation

_S_a_m_m_o_n_'_s _N_o_n_-_L_i_n_e_a_r _M_a_p_p_i_n_g

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

     One form of non-metric multidimensional scaling.

_U_s_a_g_e_:

     sammon(d, y=cmdscale(d), k=2, niter=100, trace=TRUE,
            magic=0.2, tol=1e-4)

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

       d: distance structure of the form returned by `dist',
          or a full, symmetric matrix.  Data are assumed to
          be dissimilarities or relative distances, but must
          be positive except for self-distance.

       y: An initial configuration. If none is supplied,
          `cmdscale' is used to provide the classical solu-
          tion.

       k: The dimension of the configuration.

   niter: The maximum number of iterations.

   trace: Logical for tracing optimization. Default `True'.

   magic: initial value of the step size constant in diago-
          nal Newton method.

     tol: Tolerance for stopping, in units of stress.

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

     This chooses a two-dimensional configuration to mini-
     mize the stress, the sum of squared differences between
     the input distances and those of the configuration,
     weighted by the distances, the whole sum being divided
     by the sum of input distances to make the stress scale-
     free.

     An iterative algorithm is used, which will usually con-
     verge in around 50 iterations. As this is necessarily
     an O(n^2) calculation, it is slow for large datasets.
     Further, since the configuration is only determined up
     to rotations and reflections (by convention the cen-
     troid is at the origin), the result can vary consider-
     ably from machine to machine.  In this release the
     algorithm has been modified by adding a step-length
     search (`magic') to ensure that it always goes down-
     hill.

_V_a_l_u_e_:

     Two components:

  points: A two-column vector of the fitted configuration.

  stress: The final stress achieved.

_S_i_d_e _E_f_f_e_c_t_s_:

     If trace is true, the initial stress and the current
     stress are printed out every 10 iterations.

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

     Sammon, J. W. (1969) A non-linear mapping for data
     structure analysis.  IEEE Trans. Comput.  C-18 401-409.

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

     `cmdscale', `isoMDS'

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

     library(mva)
     data(swiss)
     swiss.x <- as.matrix(swiss[, -1])
     swiss.sam <- sammon(dist(swiss.x))
     plot(swiss.sam$points, type="n")
     text(swiss.sam$points, labels=as.character(1:nrow(swiss.x)))

