Multidimensional Scaling

From Knowledge Discovery

from the Matlab statitics toolbox; see also mdscaledemo.m

function [Y,stress,disparities] = mdscale(D,p,varargin)

MDSCALE Non-Metric and Metric Multidimensional Scaling.

  Y = MDSCALE(D,P) performs non-metric multidimensional scaling on the
  N-by-N dissimilarity matrix D, and returns Y, a configuration of N
  points (rows) in P dimensions (cols).  The Euclidean distances between
  points in Y approximate a monotonic transformation of the corresponding
  dissimilarities in D.  By default, MDSCALE uses Kruskal's normalized
  STRESS1 criterion.

  You can specify D as either a full N-by-N matrix, or in upper triangle
  form such as is output by PDIST.  A full dissimilarity matrix must be
  real and symmetric, and have zeros along the diagonal and non-negative
  elements everywhere else.  A dissimilarity matrix in upper triangle
  form must have real, non-negative entries.  MDSCALE treats NaNs in D as
  missing values, and ignores those elements.  Inf is not accepted.

  You can also specify D as a full similarity matrix, with ones along the
  diagonal and all other elements less than one.  MDSCALE tranforms a
  similarity matrix to a dissimilarity matrix in such a way that
  distances between the points returned in Y approximate sqrt(1-D).  To
  use a different transformation, transform the similarities prior to
  calling MDSCALE.

 [Y,STRESS] = MDSCALE(D,P) returns the minimized stress, i.e., the
  stress evaluated at Y.

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