Triangulating topological spaces
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Topology representing networks
Neural Networks
Dynamic cell structure learns perfectly topology preserving map
Neural Computation
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
Using Growing Cell Structures for Surface Reconstruction
SMI '03 Proceedings of the Shape Modeling International 2003
Provably good sampling and meshing of surfaces
Graphical Models - Solid modeling theory and applications
Weak witnesses for Delaunay triangulations of submanifolds
Proceedings of the 2007 ACM symposium on Solid and physical modeling
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
Manifold Reconstruction in Arbitrary Dimensions Using Witness Complexes
Discrete & Computational Geometry - 23rd Annual Symposium on Computational Geometry
A growing self-organizing network for reconstructing curves and surfaces
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Data clustering: 50 years beyond K-means
Pattern Recognition Letters
Growing self-reconstruction maps
IEEE Transactions on Neural Networks
Manifold reconstruction using tangential Delaunay complexes
Proceedings of the twenty-sixth annual symposium on Computational geometry
IEEE Transactions on Neural Networks
`Neural-gas' network for vector quantization and its application to time-series prediction
IEEE Transactions on Neural Networks
Topological estimation using witness complexes
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Clustering of gene expression profiles applied to marine research
IWANN'13 Proceedings of the 12th international conference on Artificial Neural Networks: advances in computational intelligence - Volume Part I
| Hi-index | 0.00 |
Competitive Hebbian Learning (CHL) (Martinetz, 1993) is a simple and elegant method for estimating the topology of a manifold from point samples. The method has been adopted in a number of self-organizing networks described in the literature and has given rise to related studies in the fields of geometry and computational topology. Recent results from these fields have shown that a faithful reconstruction can be obtained using the CHL method only for curves and surfaces. Within these limitations, these findings constitute a basis for defining a CHL-based, growing self-organizing network that produces a faithful reconstruction of an input manifold. The SOAM (Self-Organizing Adaptive Map) algorithm adapts its local structure autonomously in such a way that it can match the features of the manifold being learned. The adaptation process is driven by the defects arising when the network structure is inadequate, which cause a growth in the density of units. Regions of the network undergo a phase transition and change their behavior whenever a simple, local condition of topological regularity is met. The phase transition is eventually completed across the entire structure and the adaptation process terminates. In specific conditions, the structure thus obtained is homeomorphic to the input manifold. During the adaptation process, the network also has the capability to focus on the acquisition of input point samples in critical regions, with a substantial increase in efficiency. The behavior of the network has been assessed experimentally with typical data sets for surface reconstruction, including suboptimal conditions, e.g. with undersampling and noise.