XGvis uses multidimensional scaling (MDS) to map a set of objects
to points in k-space such that:
   
  dissimilarity( object i, object j ) ~ distance( point i, point j )

This is made precise by minimizing the above Stress function.

The parameters of the function are:

D = target distance matrix 
    This is either supplied as a matrix of dissimilarities or
    distances, or it uses the shortest-path metric if a discrete
    graph is given in terms of a links file.

p = exponent of the power transformation of D 

l = Minkowski norm used to calculate the current interpoint 
    distances (l=2 corresponds to the Euclidean metric on k-space)

r = residual power applied to the difference between the target
    distance D and the interpoint distances

T = threshold above which dissimilarities are removed from the 
    stress function

The value of the stress function is plotted as a number generally between
zero and one.

Below the plot of the stress function is a barplot of the distribution
of D^p.  As you change p, this plot is updated.  Use the left mouse
button to set the threshold T used in the stress function: the solid
bars are below the threshold and represent the distances used in MDS;
the hollow bars correspond to pairs of points that are ignored.

Other parameters available on the control panel are

Dimension (k): the dimensionality of the space into which the data are
  being mapped.  The default is 3D.  Examine your point configurations
  with 3D rotations or grand tours in XGobi.

Stepsize: the size of the step taken to bring x[i] and x[j] closer
  together or to push them farther apart.  You might start with a
  large stepsize and then reduce it once the structure begins to
  stabilize.  You can also increase it suddenly in a form of
  interactive "simulated annealing," to jump out of a local minimum
  when you think there might be a lower minimum elsewhere.

MDS within subgroups: If you have subgroups in the data that you would
  like to handle separately from one another, then brush them using
  XGobi.  Then select this button and restart "Run MDS."  Now only
  distances between points with the same glyph and color will be
  considered.

MDS casewise: If you would like to investigate the behavior of a
  single case, or a small group of cases, then use XGobi to add
  persistent labels to those cases.  Then select this button and
  restart "Run MDS."  Now only distances between pairs of points
  including one of the labelled points will be considered.  (This
  feature can be used in conjunction with brush groups.  Then only
  distances between pairs of points with the same color and glyph AND
  within the same brush group will be considered.)

Shepard diagram:  Launch an XGobi containing a plot of D^p vs
  the configuration distances.  You can first specify that you
  would like to start XGobi with an option:  its initial display
  can be a random sample of the data.  That is, all the data will
  be written out to a file (configd0.dat, configd1.dat, ...) and
  then read in by XGobi, but a subset may be chosen for display.
  (See Subset Data on the XGobi Tools Menu.)

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Input files:

One of these three is required: 
- a file of dissimilarities,
- a file of starting positions,
- a file of links.

Usage:

  xgvis -dist distsfile
  xgvis -pos posfile
    A distance matrix of full dimensionality, N by N, is generated.

  xgvis -links linksfile
    The distance matrix is populated with link distances.  See the
    XGobi manual page (filename.lines) for a description of this file
    format.

If files of links and positions are both supplied, link distances are
used and the positions are used only for starting positions.

Additional optional files:

  -labels labelfile
  -glyphs glyphfile
  -pointcolors colorfile
  -linecolors colorfile

See the XGobi manual page for descriptions of these files.  For a
description of glyphfile, see filename.glyphs; for labelfile, see
filename.row; for pointcolors, see filename.colors; for linecolors,
see filename.linecolors.  Another method for reading these files into
XGvis is by using the "Read" function from "File" in XGobi.

The input file can contain missing values, represented by the strings
"na" or "NA" or "."  By making use of specific missing value patterns,
XGvis can be used to perform "multidimensional unfolding."