%0 Conference Paper %1 GoodhillEtAl1995 %A Goodhill, G.J. %A Finch, S. %A Sejnowski, T.J. %B Proc. 2nd Joint Symp. on Neural Computation %D 1995 %K dimensionalityreduction mapformation selforganization %P 191--202 %T A unifying measure for neighbourhood preservation in topographic mappings %X In this paper, the abstract computational principles underlying topographic maps are discussed. We give a definition of a “perfectly neighbourhood preserving” map, which we call a topographic homeomorphism, and we prove that this has certain desirable properties. It is argued that when a topographic homeomorphism does not exist (the usual case), many equally valid choices are available for quantifying the quality of a map. We introduce a particular measure that encompasses several previous proposals, and discuss its relation to other work. This formulation of the problem sets it within the well-known class of quadratic assignment problems.

@inproceedings{GoodhillEtAl1995, abstract = {In this paper, the abstract computational principles underlying topographic maps are discussed. We give a definition of a “perfectly neighbourhood preserving” map, which we call a topographic homeomorphism, and we prove that this has certain desirable properties. It is argued that when a topographic homeomorphism does not exist (the usual case), many equally valid choices are available for quantifying the quality of a map. We introduce a particular measure that encompasses several previous proposals, and discuss its relation to other work. This formulation of the problem sets it within the well-known class of quadratic assignment problems. }, added-at = {2008-05-12T14:04:26.000+0200}, author = {Goodhill, G.J. and Finch, S. and Sejnowski, T.J.}, biburl = {https://www.bibsonomy.org/bibtex/29b9a2eae063f9ce20f09246484d8db9d/tmalsburg}, booktitle = {Proc. 2nd Joint Symp. on Neural Computation}, interhash = {39a5ec4759d9bebf5c43f19ebdbef74e}, intrahash = {9b9a2eae063f9ce20f09246484d8db9d}, keywords = {dimensionalityreduction mapformation selforganization}, pages = {191--202}, timestamp = {2008-05-12T14:05:15.000+0200}, title = {{A unifying measure for neighbourhood preservation in topographic mappings}}, year = 1995 }