Time Series Prediction Based On The Online Kernel Extreme Learning Machine

Time series data is a kind of widely used data format, which is derived from various practical applications. It can provide a reliable basis for the government and enterprises to make the decision and plan through the mining of time series data, which has important practical significance.Extreme learning machine(ELM) algorithm is a new machine learning algorithm in recent years. Compared with the traditional machine learning algorithm, it has the advantages of simple structure, fast learning speed and good global optimization ability. It shows great potential in complex system modeling, real-time online prediction and large scale samples learning. On the basis of Reduced Kernel ELM(RKELM) algorithm and Online Sequential ELM(OS-ELM) algorithm, a new algorithm of Online Sequential Kernel ELM(OS-KELM) algorithm is proposed, finally the adaptive ensemble online kernel ELM(AE-OSKELM) algorithm is designed and implemented for online prediction of time series according to the OS-KELM algorithm’s improvement for related problems and time series data’s timeliness characteristic. The main work of this paper is as follows:Firstly, this paper introduces the concept, theoretical foundation, training algorithm and the research status of the extreme learning machine, and then divides into five kinds: the structure growth extreme learning machine, the structural decline extreme learning machine, the regular extreme learning machine, the online extreme learning machine, and the kernel extreme learning machine. And the several typical training algorithms is given for each kind of extreme learning machine, their advantages and disadvantages are also analyzed.Secondly, on the basis of RKELM algorithm and OS-ELM algorithm, this paper proposes a new algorithm named OS-KELM algorithm. At the same time, the timeliness characteristic of time series data is introduced into the training of OS-KELM algorithm, and the penalty weight is also introduced to distinguish the prediction contribution for different historical data, it can give higher weights to the latest historical data according to regulating penalty weight. However, as a result of the latest historical data may be noise data, the setting of penalty weight should not be fixed but it should vary adaptively according to the characteristics of the current data, this paper introduces the calculation formula of penalty weight to avoid the occurrence of such errors according to the change of the mean and variance of the data at time t and t+1.But the prediction accuracy of the algorithm is affected by the parameters of the kernel function, This paper proposes an improved FOA algorithm to optimize the OS-KELM algorithm according to the principle of the fruit fly optimization algorithm(FOA) and the characteristics of the OS-KELM algorithm. At last, because the OS-KELM algorithm extracts partial data for operation of the kernel matrix from the training data in a certain proportion, which will affect the generalization ability of OS-KELM algorithm, So this paper proposes the adaptive ensemble online kernel learning machine to improve the stability of the algorithm according to choosing the OS-KELMs which have the better generalization ability and the higher prediction accuracy.Finally, this paper uses the matlab2009 b platform to program the AE-OSKELM algorithm, and compares with the classical machine learning algorithms such as LS-SVM, ELM and BPNN to verify the effectiveness of the proposed algorithm about time complexity and prediction accuracy. In addition, it discusses the setting of the algorithms parameter according to the simulation experiment before making contrast experiments, such as the hidden layer node number of BPNN, ELM and OSELM algorithm and the relationships of time complexity, prediction accuracy and the sample proportion of kernel matrix in AE-OSKELM algorithm. At last, the proposed algorithm has good anti-noise ability, and can fit the simulation data, UCI data set and real stock price data well, it has the least prediction error in the same time complexity.On the one hand, it provides a reference for the further research through the summary of the theory of extreme learning machine. At the same time, it enriches theoretical research of extreme learning machine by proposing AE-OSKELM algorithm. On the other hand, the AE-OSKELM algorithm is proposed according to the combination of the online kernel extreme learning machine and time series prediction, and the paper also verify validity of the AE-OSKELM algorithm through a large number of experiments. It provides a better prediction method for forecasting the stock price and other time series data.