Inproceedings,
Data Extrapolation Using Genetic Programming to Matrices Singular Values Estimation
Proceedings of the 2006 IEEE Congress on Evolutionary Computation, page 3227--3230. Vancouver, BC, Canada, IEEE Press, (16-21 July 2006)
Abstract
In mathematical models where the dimensions of the
matrices are very large, the use of classical methods
to compute the singular values is very time consuming
and requires a lot of computational resources. In this
way, it is necessary to find new faster methods to
compute the singular values of a very large matrix. We
present a method to estimate the singular values of a
matrix based on Genetic Programming (GP). GP is an
approach based on the evolutionary principles of the
species. GP is used to make extrapolations of data out
of sample data. The extrapolations of data are achieved
by irregularity functions which approximate very well
the trend of the sample data. GP produces from just
simple's functions, operators and a fitness function,
complex mathematical expressions that adjust smoothly
to a group of points of the form (xi, yi). We obtain
amazing mathematical formulas that follow the behaviour
of the sample data. We compare our algorithm with two
techniques: the linear regression and non linear
regression approaches. Our results suggest that we can
predict with some percentage of error the largest
singular values of a matrix without computing the
singular values of the whole matrix and using only some
random selected columns of the matrix.
