isoMDS                 package: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, maxit = 50, trace = TRUE, tol = 1e-3)

_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 solution. The dimension of the
          initial configuration determines that of the answer. 

       k: The desired dimension for the solution, passed to 'cmdscale'. 

   maxit: The maximum number of iterations. 

   trace: Logical for tracing optimization. Default 'TRUE'. 

     tol: convergence tolerance. 

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

     This chooses a k-dimensional (default k = 2) configuration to
     minimize the stress, the square root of the ratio of the sum of
     squared differences between the input distances 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 converge 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 centroid is at the origin), the result can vary
     considerably 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, 2001) _Multidimensional
     Scaling_. Chapman & Hall.

     Ripley, B. D. (1996) _Pattern Recognition and Neural Networks_.
     Cambridge University Press.

     Venables, W. N. and Ripley, B. D. (2002) _Modern Applied
     Statistics with S._ Fourth edition.  Springer.

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

     'cmdscale', 'sammon'

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

     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$points)
     plot(swiss.sh, pch = ".")
     lines(swiss.sh$x, swiss.sh$yf, type = "S")

