Fuzzy Integral-Based Kernel Regression Ensemble and Its Application

Abstract

Similar to ensemble learning for classification, regression ensemble also tries to improve the prediction accuracy through combining several “weak” estimators that are usually high-variance and thus unstable. In this chapter, the authors propose a new scheme of fusing the weak Priestley-Chao Kernel Estimators (PCKEs) based on Choquet fuzzy integral, which differs from all the existing models of regressor fusion. The new scheme uses Choquet fuzzy integral to fuse several target outputs from different PCKEs, in which the optimal bandwidths are obtained with cross-validation criteria. The key of applying fuzzy integral to PCKE fusion is the determination of fuzzy measure. Considering the advantage of Particle Swarm Optimization (PSO) algorithm on convergence rate, the authors use three different PSO algorithms (i.e., Standard PSO [SPSO], Gaussian PSO [GPSO], and GPSO with Gaussian Jump [GPSOGJ]) to determine the general and ? fuzzy measures. The experimental results on the standard testing functions and practical Fourier Transform Infrared Spectroscopy (FTIR) datasets show that the new paradigm for regression ensemble based on fuzzy integral is more accurate and stable in comparison with any individual PCKE and the Basic Ensemble Method (BEM). This demonstrates the feasibility and effectiveness of the proposed regression ensemble model.