There has been many methods in constructing neural network (NN) ensembles,where the method of simultaneous training has succeed in generalization performance and efficiency.But just like regular methods of constructing NN ensembles,it follows the two steps,first training component networks,and then combining them.As the two steps being independent,an assumption is used to facilitate interactions among NNs during the training stage.This paper presents a compact ensemble method which integrates the two steps of ensemble construction into one step by attempting to train individual NNs in an ensemble and weigh the individual members adaptively according to their individual performance in the same learning process.This provides an opportunity for the individual NNs to interact with each other based on their real contributions to the ensemble.The classification performance of NN compact ensemble (NNCE) was validated through some benchmark problems in machine learning,including Australian credit card assessment,pima Indians diabetes,heart disease,breast cancer and glass.Compared with other ensembles,the classification error rate of NNCE can be decreased by 0.45% to 68%.In addition,the NNCE was applied to fault diagnosis for rolling element bearing.The 11 time-domain statistical features are extracted as the properties of data,and the NNCE is employed to classify the data.With the results of several experiments,the compact ensemble method is shown to give good generalization performance.The compact ensemble method can recognize the different fault types and various fault degrees of the same fault type.
