@inproceedings{GoodhillSejnowski1996,
title = {{Quantifying neighbourhood preservation in topographic mappings}},
author = {G. Goodhill and S. Finch and T. Sejnowski},
booktitle = {Proceedings of the 3rd Joint Symposium on Neural Computation},
year = {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.
},
keywords = {brainconnectivity dimensionalityreduction }
}
::