Fast Ensemble of Separating HyperPlanes for Nonlinear Classification

Although the function set of Linear HyperPlane (LHP) obtained from the Separating HyperPlane (SHP) method based on direct marketing campaigns has a very low Vapnik-Chervonenkis dimension equal to 9 or lower and the corresponding optimized LHP can fast detect unseen instance and preserve users privacy, it is inefficient in training speed, sensitive to training examples and not able to apply to nonlinear datasets. For overcoming these drawbacks as above, a nonlinear classification approach is proposed in this paper, which is suitable for large datasets and called Fast Ensemble of Separating HyperPlane (FE-SHP). First, the original training data is split into several subsets and their suboptimal LHPs are respectively constructed. Then, the nonlinear ensembling effects of suboptimal LHPs are enhanced by introducing an optimized weight vector after improving their nonlinear capabilities with Radical Basis Function (RBF). Finally, the related parameters are solved by the gradient descent method to maximize a log likelihood function which is the cross-entropy error of training data following the ensembling output of suboptimal LHPs being mapped probabilities. Experimental results on UCI demonstrate that the presented FE-SHP obtains competitive effectiveness for large datasets.