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

01/07/2010
by   Alexander N. Gorban, et al.
0

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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 5

04/21/2013

A novice looks at emotional cognition

Modeling emotional-cognition is in a nascent stage and therefore wide-op...
02/11/2013

Geometrical complexity of data approximators

There are many methods developed to approximate a cloud of vectors embed...
09/02/2008

Principal Graphs and Manifolds

In many physical, statistical, biological and other investigations it is...
03/22/2006

Topological Grammars for Data Approximation

A method of topological grammars is proposed for multidimensional data ...
05/21/2003

Neural network modeling of data with gaps: method of principal curves, Carleman's formula, and other

A method of modeling data with gaps by a sequence of curves has been dev...
04/20/2018

Robust and scalable learning of data manifolds with complex topologies via ElPiGraph

We present ElPiGraph, a method for approximating data distributions havi...
01/27/2021

Discovering dependencies in complex physical systems using Neural Networks

In todays age of data, discovering relationships between different varia...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.