Beyond The Concept of Manifolds: Principal Trees, Metro Maps, and Elastic Cubic Complexes

@article{Gorban2008BeyondTC,
  title={Beyond The Concept of Manifolds: Principal Trees, Metro Maps, and Elastic Cubic Complexes},
  author={Alexander N. Gorban and Neil R. Sumner and Andrei Yu. Zinovyev},
  journal={Scopus},
  year={2008},
  pages={219-237}
}
Multidimensional data distributions can have complex topologies and variable local dimensions. To approximate complex data, we propose a new type of low-dimensional ``principal object'': a principal cubic complex. This complex is a generalization of linear and non-linear principal manifolds and includes them as a particular case. To construct such an object, we combine a method of topological grammars with the minimization of an elastic energy defined for its embedment into multidimensional… Expand
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