Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Topology representing networks
Neural Networks
Dynamic cell structure learns perfectly topology preserving map
Neural Computation
Self-organizing maps
Surface reconstruction by Voronoi filtering
Proceedings of the fourteenth annual symposium on Computational geometry
A self-organising network that grows when required
Neural Networks - New developments in self-organizing maps
AIM@SHAPE Project Presentation
SMI '04 Proceedings of the Shape Modeling International 2004
Topology for Computing (Cambridge Monographs on Applied and Computational Mathematics)
Topology for Computing (Cambridge Monographs on Applied and Computational Mathematics)
Geometry and Topology for Mesh Generation (Cambridge Monographs on Applied and Computational Mathematics)
Weak witnesses for Delaunay triangulations of submanifolds
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Manifold reconstruction in arbitrary dimensions using witness complexes
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Reconstruction using witness complexes
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Three-dimensional surface reconstruction using meshing growing neural gas (MGNG)
The Visual Computer: International Journal of Computer Graphics
Topological estimation using witness complexes
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
| Hi-index | 0.00 |
Self-organizing networks such as Neural Gas, Growing Neural Gas and many others have been adopted in actual applications for both dimensionality reduction and manifold learning. Typically, the goal in these applications is obtaining a good estimate of the topology of a completely unknown subspace that can be explored only through an unordered sample of input data points. In the approach presented here, the dimension of the input manifold is assumed to be known in advance. This prior assumption can be harnessed in the design of a new, growing self-organizing network that can adapt itself in a way that, under specific conditions, will guarantee the effective and stable recovery of the exact topological structure of the input manifold.