Data Extrapolation Using Genetic Programming to Matrices Singular Values Estimation

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.