A heuristic algorithm for pattern identification in large multivariate analysis of geophysical data sets

Abstract

This paper aims to present a heuristic algorithm with factor analysis and a local search optimization system for pattern identification problems as applied to large and multivariate aero-geophysical data. The algorithm was developed in MATLAB code using both multivariate and univariate methodologies. Two main analysis steps are detailed in the MATLAB code: the first deals with multivariate factor analysis to reduce the problem of dimension, and to orient the variables in an independent and orthogonal structure; and the second with the application of a novel local research optimization system based on univariate structure. The process of local search is simple and consistent because it solves a multivariate problem by summing up univariate and independent problems. Thus, it can reduce computational time and render the efficiency of estimates independent of the data bank. The aero-geophysical data include the results of the magnetometric and gammaspectrometric (TC, K, Th, and U channels) surveys for the Santa Maria region (RS, Brazil). After the classification, when the observations are superimposed on the regional map, one can see that data belonging to the same subspace appear closer to each other revealing some physical law governing area pattern distribution. The analysis of variance for the original variables as functions of the subspaces obtained results in different mean behaviors for all the variables. This result shows that the use of factor transformation captures the discriminative capacity of the original variables. The proposed algorithm for multivariate factor analysis and the local search system open up new challenges in aero-geophysical data handling and processing techniques.