A sparse deep belief network with efficient fuzzy learning framework.

Deep belief network (DBN) is one of the most feasible ways to realize deep learning (DL) technique, and it has been attracting more and more attentions in nonlinear system modeling. However, DBN cannot provide satisfactory results in learning speed, modeling accuracy and robustness, which is mainly caused by dense representation and gradient diffusion. To address these problems and promote DBN's development in cross-models, we propose a Sparse Deep Belief Network with Fuzzy Neural Network (SDBFNN) for nonlinear system modeling. In this novel framework, the sparse DBN is considered as a pre-training technique to realize fast weight-initialization and to obtain feature vectors. It can balance the dense representation to improve its robustness. A fuzzy neural network is developed for supervised modeling so as to eliminate the gradient diffusion. Its input happens to be the obtained feature vector. As a novel cross-model, SDBFNN combines the advantages of both pre-training technique and fuzzy neural network to improve modeling capability. Its convergence is also analyzed as well. A benchmark problem and a practical problem in wastewater treatment are conducted to demonstrate the superiority of SDBFNN. The extensive experimental results show that SDBFNN achieves better performance than the existing methods in learning speed, modeling accuracy and robustness.