Paper available

[geoff@salk.edu]

The following paper is available via

      ftp://ftp.cnl.salk.edu/pub/geoff/goodhill_sejnowski_96.ps.Z
or
      http://www.cnl.salk.edu/~geoff

   QUANTIFYING NEIGHBOURHOOD PRESERVATION IN TOPOGRAPHIC MAPPINGS

         Geoffrey J. Goodhill & Terrence J. Sejnowski
                      The Salk Institute

 From: Proceedings of the 3rd Joint Symposium on Neural Computation, 1996

                            ABSTRACT

Mappings that preserve neighbourhood relationships are important in
many contexts, from neurobiology to multivariate data analysis.  It is
important to be clear about precisely what is meant by preserving
neighbourhoods. At least three issues have to be addressed: how
neighbourhoods are defined, how a perfectly neighbourhood preserving
mapping is defined, and how an objective function for measuring
discrepancies from perfect neighbourhood preservation is defined.  We
review several standard methods, and using a simple example mapping
problem show that the different assumptions of each lead to
non-trivially different answers.  We also introduce a particular
measure for topographic distortion, which has the form of a quadratic
assignment problem. Many previous methods are closely related to this
measure, which thus serves to unify disparate approaches.

22 pages, uncompressed postscript = 1.1MB

NOTE: I advertised a tech report with the same title on this list last
      year: the new paper contains more recent work.