Extreme Learning Machine For Multivariate Time Series Prediction

Not only can time series reflect the developments of astronomy,finance,biomedicine,control science and marine science,but also can it predict some phenomena by exploring the laws of their changes.With the deep researching of time series analysis,many linear and nonlinear time series prediction methods have been proposed at home and abroad achieving a good result in the process of execution,while most of them are proposed for predicting univariate time series.However,the time series data collected from the real world is often impacted by many factors instead one,thus the study of the multivariate time series prediction is more realistic significance.Because the characteristic of multi-noise,multi-scale and variable correlation in multivariate time series data is different from the univariate time series,the existing univariate time series prediction methods can not predict multivariate time series directly,which makes the study of the multivariate time series prediction important theoretical value.Three kinds of prediction models using the extreme learning machine as their learning tool are proposed for multivariate time series prediction research in this paper.The main contributions are as follows:1.In the process of learning parameters,ELM only takes the known samples into account.However,the number of the samples is insufficient in the practical application,thus ELM only considers the information carried by the known samples can not meet the requirement of prediction accuracy.To solve the problem,the latent extreme learning machine(LELM)is proposed to consider both the known and unknown information carried by the samples in the feature space of ELM.Simulation results in multivariate time series show that LELM can improve the prediction ability of extreme learning machine effectively.2.In multivariate time series prediction based on extreme learning machine(ELM),the prediction precision will be reduced by converting matrix samples to vectors.To solve the problem,a multivariate time series prediction model,SVDELM,based on singular value decomposition and extreme learning machine is proposed to suit for the matrix input,which adds a SVD dimension reduction layer between the hidden layer and the output layer of the ELM.Simulation results on chaotic multivariate time series and stock multivariate time series show that the SVDELM is an effective prediction model for multivariate time series.3.SVDELM and two-dimensional extreme learning machine(2D-ELM)are prediction models based on matrix input.However the original data information will lose as SVDELM reduces the dimension of the feature space or 2D-ELM reduces the dimension of the input samples during projection procedure.To solve the above problem,we propose a prediction model,the improved two-dimensional extreme learning machine(I2D-ELM)without dimension reduction.Simulation results show that I2D-ELM can greatly improve the accuracy of multivariate time series forecasting model.