An integrated neural network with nonlinear output structure for interval-valued data

In this paper, an integrated model combining interval deep belief network (IDBN) and neural network with nonlinear weights, called IDBN-NN, is proposed for interval-valued data modeling. Firstly, the IDBN with variable learning rate is designed to initialize parameters of each sub-model. Based on a modified contrastive divergence algorithm the least square method is adopted to identify the coefficients of nonlinear weights in the output layer. Then, to improve the modeling accuracy, the Fuzzy C-Means (FCM) method and the Particle Swarm Optimization (PSO) algorithm are applied to tune the weights of sub-models. Though each sub-model can capture the nonlinear feature of the original system, by intersecting cut sets the synthesizing modeling scheme can further improve the performance of the proposed model. Some numerical examples show that the IDBN-NN with nonlinear output structure can achieve higher accuracy than some interval-valued data modeling methods.