Principal manifolds and graphs in practice: from molecular biology to dynamical systems

Details Principal manifolds and graphs in practice: from molecular biology to dynamical systems Principal manifolds and graphs in practice: from molecular biology to dynamical systems

2010-01-07

arxiv.org/abs/1001.1122v2

International Journal of Neural Systems, Vol. 20, No. 3 (2010) 219-232

Computer Science

Neural and Evolutionary Computing

12 pages, 9 figures

Scientific paper

10.1142/S0129065710002383

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.

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