Dual possibilistic regression analysis using support vector networks

This study proposes a novel and efficient dual regression model for possibilistic regression analysis that incorporates the principles of support vector machine (SVM) theory. The dual regression model, which comprises an upper model and a lower model, approximates the observed fuzzy phenomena from the outside and inside directions, respectively, such that the inclusion relationship between those two models holds. The proposed dual regression model better explains the inherent vagueness that exists in a given dataset. It provides the outer and inner bounds for the estimated vagueness region, and allows an estimation of the degree of confidence in the predicted fuzzy output. Using the principles for a twin support vector machine (TSVM), the upper- and lower models are estimated by solving two smaller SVM-type quadratic programming problems (QPPs), instead of a single larger QPP. This strategy significantly increases the learning speed for the proposed algorithm. The structural risk minimization principle of SVM makes the proposed method to yield better generalization ability. The kernel function method offers a model-independent framework for the proposed dual regression model. This paper focuses on the class of radial kernels, which enables the proposed method to conquer the problem of increasing spreads. The radial kernel also gives the proposed method a unified framework that allows both crisp and fuzzy inputs. The experimental results verify the effectiveness and efficiency of the proposed method. In comparison with previous SVM-based dual regression model, the proposed approach significantly improves the sparsity, prediction speed, and training speed.