Rough Set-Based Dimensionality Reduction for Multivariate Adaptive Regression Splines

Abstract

Dimensionality is an obstacle for many potentially powerful machine learning techniques. Widely approved and otherwise elegant methodologies exhibit relatively high complexity. This limits their applicability to real world applications. Friedman’s Multivariate Adaptive Regression Splines (MARS) is a function approximator that produces continuous models of multi-dimensional functions using recursive partitioning and multidimensional spline curves that are automatically adapted to the data. Despite this technique’s many strengths, it, too, suffers from the dimensionality problem. Each additional dimension of a hyperplane requires the addition of one dimension to the approximation model, and an increase in the time and space required to compute and store the splines. Rough set theory can reduce dataset dimensionality as a preprocessing step to training a learning system. This paper investigates the applicability of the Rough Set Attribute Reduction (RSAR) technique to MARS in an effort to simplify the models produced by the latter and decrease their complexity. The paper describes the techniques in question and discusses how RSAR can be integrated with MARS. The integrated system is tested by modelling the impact of pollution on communities of several species of river algae. These experimental results help draw conclusions on the relative success of the integration effort.