Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio