Regression And Prediction Of Interval-valued Model Based On Restricted Boltzmann Machine

In many real-world application fields,fuzzy data or interval-valued data is often used to describe attributes' uncertainty due to the complexity and indeterminacy of observing objects.In this thesis,it mainly aims at studying interval modeling and discusses respectively model establishment based on different types of input-output data.The main contents of this thesis are as follows:Firstly,interval deep belief network-feedforward neural network on the basis of Taylor's expansion in terms of interval input-interval output data set is proposed,which can be used to initialize feedforward neural network's parameters by introducing training mechanism of restricted boltzmann machine and output layer's weights are represented by Taylor's expansion to reduce network size.Fuzzy c-means clustering algorithm and the concept of cut are used to repartition data so as to establish multiple local interval models and then they are integrated with weights to improve the performance of the model.A series of simulations are carried out to verify the validity of the proposed model.Secondly,considering the case that input data and output data are all crisp,both numerical approximation and the information inclusion degree are taken into account.On this basis,a fuzzy model based on cubic spline function is put forward for interval regression analysis on this type of data.Spline function parameters are identified by constructing neural network model and the gradient descent algorithm is used to update the interval weights.Correspondingly,a modified target function is used to improve the performance of the estimated interval.The simulation results show that the proposed interval regression model can not only have the very good approximation effect of nonlinear function but obtain an interval including enough information.Finally,as for the case of crisp input-interval output data,an ensemble model on the base of RBM is put forward.Input data are converted to attributes of another feature space by means of superior learning ability of restricted boltzmann machine.Then the obtained new attribute set and the original input are reconstituted to generate component learners that are integrated to set up the ensemble model.The superior is determined by comparing the learning abilities of various ensemble models derived from different weak learners.Meanwhile,the simulation results in comparison with classical interval neural network modeling also show that the proposed integrated model based on RBM can improve the modeling accuracy to a certain extent.