Modularization of xcsf for multiple output dimensions

Abstract

XCSF approximates function surfaces by evolving a suitable clustering of the input space, so that a simple -- typically linear -- predictor yields sufficient accuracy in each cluster. With an increasing number of distinct output dimensions, however, the accuracy of local predictions typically decreases. We analyze the performance of a single XCSF instance and compare it to the performance of a multiple-instance XCSF, where each instance predicts one dimension of the output. We show that dependent on the problem at hand, the multiple-instance XCSF approach is highly advantageous. In particular, we show that the more local linearity structures differ, the more a modularized approximation by multiple XCSF instances pays off. In fact, if modularization is not applied, the problem complexity may increase exponentially in the number of approximately orthogonally-structured output dimensions. To relate these results also to current XCSF application options, we show that the multiple-instance XCSF approach can also be applied to the problem of learning a compact model of the Jacobian of the forward-kinematics of a seven degree of freedom anthropomorphic robot arm for inverse robot arm control in simulation.