Principal manifolds and graphs in practice: from molecular biology to dynamical systems.
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 mappings of datasets into the spaces of lower dimension. The examples are taken from comparative political science, from analysis of high-throughput data in molecular biology, from analysis of dynamical systems.
Gorban
Alexander N
AN
Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, UK. ag153@le.ac.uk
Zinovyev
Andrei
A
D000465:Algorithms; D019295:Computational Biology / Q000379:methods / Q000639:trends; D008959:Models, Neurological; D008962:Models, Theoretical; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics; D049490:Systems Biology / Q000379:methods