

isoMDS(MASS)                                 R Documentation

_K_r_u_s_k_a_l_'_s _N_o_n_-_m_e_t_r_i_c _M_u_l_t_i_d_i_m_e_n_s_i_o_n_a_l _S_c_a_l_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_:

     isoMDS(d, y = cmdscale(d, k), k = 2, niter = 50, trace = TRUE)

_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'.

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

     This chooses a two-dimensional configuration to mini-
     mize the stress, the square root of the ratio of the
     the sum of squared differences between the input dis-
     tances and those of the configuration to the sum of
     configuration distances squared. However, the input
     distances are allowed a monotonic transformation.

     An iterative algorithm is used, which will usually con-
     verge in around 10 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.

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

     Two components:

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

  stress: The final stress achieved (in percent).

_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 5 iterations.

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

     T. F. Cox and M. A. A. Cox (1994) Multidimensional
     Scaling.  Chapman  Hall.

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

     `cmdscale', `sammon'

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

     library(mva) # for dist
     data(swiss)
     swiss.x <- as.matrix(swiss[, -1])
     swiss.dist <- dist(swiss.x)
     swiss.mds <- isoMDS(swiss.dist)
     plot(swiss.mds$points, type="n")
     text(swiss.mds$points, labels=as.character(1:nrow(swiss.x)))
     swiss.sh <- Shepard(swiss.dist, swiss.mds$points)
     plot(swiss.sh)
     lines(swiss.sh$x, swiss.sh$yf, type="S")

