2003 -03 -25
10 :15 at Method of Elastic Maps and Its

Method of Elastic Maps and Its Applications

Andrey Zinovyev

IHES, France

We live in the epoch of exponential growth of information. Internet, Intranet nets, local computers contain a huge amount of information databases and their number grows continually. The question is how to organize all this information, and, how to represent it. In this talk we describe method of elastic maps, which can help in this problem. It allows finding useful projections of multidimensional data into non-linear low-dimensional spaces. Mathematically speaking, method of elastic maps allows to construct efficiently 1D, 2D and 3D non-linear grid approximations to the principal manifolds with different topology (piece of plane, sphere, torus etc.) and to project data onto it. Using this method, it is possible to find smooth non-linear approximations of a finite set of points in R N , in linear time. We describe the idea of the method and demonstrate its applications as well as the software, which implements it.