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.
|Number of pages||8|
|Journal||Lecture Notes in Computer Science|
|State||Published - 2005|
|Event||6th International Conference on Intelligent Data Engineering and Automated Learning - IDEAL 2005 - Brisbane, Australia|
Duration: Jul 6 2005 → Jul 8 2005