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Springer, Lecture Notes in Computer Science, p. 335-342, 2005

DOI: 10.1007/11508069_44

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Differential Priors for Elastic Nets

Proceedings article published in 2005 by Miguel Á. Carreira-Perpinan, Peter Dayan, Geoffrey J. Goodhill ORCID
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This paper is available in a repository.

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Abstract

The elastic net and related algorithms, such as generative topographic mapping, are key methods for discretized dimension-reduction problems. At their heart are priors that specify the expected topological and geometric properties of the maps. However, up to now, only a very small subset of possible priors has been considered. Here we study a much more general family originating from discrete, high-order derivative operators. We show theoretically that the form of the discrete approximation to the derivative used has a crucial influence on the resulting map. Using a new and more powerful iterative elastic net algorithm, we confirm these results empirically, and illustrate how different priors affect the form of simulated ocular dominance columns.