Chen, Sheng, Hong, Xia and Harris, Chris J.
Particle swarm optimization aided orthogonal forward regression for unified data modelling.
IEEE Transactions on Evolutionary Computation, 14, (4), . (doi:10.1109/TEVC.2009.2035921).
We propose a uni?ed data modeling approach that is equally applicable to supervised regression and classi?cation applications, as well as to unsupervised probability density function estimation. A particle swarm optimization (PSO) aided orthogonal forward regression (OFR) algorithm based on leave-one-out (LOO) criteria is developed to construct parsimonious radial basis function (RBF) networks with tunable nodes. Each stage of the construction process determines the center vector and diagonal covariance matrix of one RBF node by minimizing the LOO statistics. For regression applications, the LOO criterion is chosen to be the LOO mean square error, while the LOO misclassi?cation rate is adopted in two-class classi?cation applications. By adopting the Parzen window estimate as the desired response, the unsupervised density estimation problem is transformed into a constrained regression problem. This PSO aided OFR algorithm for tunable-node RBF networks is capable of constructing very parsimonious RBF models that generalize well, and our analysis and experimental results demonstrate that the algorithm is computationally even simpler than the ef?cient regularization assisted orthogonal least square algorithm based on LOO criteria for selecting ?xed-node RBF models. Another signi?cant advantage of the proposed learning procedure is that it does not have learning hyperparameters that have to be tuned using costly cross validation. The effectiveness of the proposed PSO aided OFR construction procedure is illustrated using several examples taken from regression and classi?cation, as well as density estimation applications
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