# Principal Manifolds and Graphs in Practice: from Molecular Biology to Dynamical Systems

@article{Gorban2010PrincipalMA, title={Principal Manifolds and Graphs in Practice: from Molecular Biology to Dynamical Systems}, author={Alexander N. Gorban and A. Zinovyev}, journal={International journal of neural systems}, year={2010}, volume={20 3}, pages={ 219-32 } }

We present several applications of non-linear data modeling, using principal manifolds and principal graphs constructed using the metaphor of elasticity (elastic principal graph approach). These approaches are generalizations of the Kohonen's self-organizing maps, a class of artificial neural networks. On several examples we show advantages of using non-linear objects for data approximation in comparison to the linear ones. We propose four numerical criteria for comparing linear and non-linear… Expand

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