| Online time series prediction is a hot research topic which needs to onlinepredict for large, non-linear, random samples, and has high requirements on both ofthe prediction accuracy and efficiency. KRLS (Kernel Recursive Least Square)algorithm has advantages such as fast convergent ability, low computationalcomplexity and simple modeling character, so that it is suitable for online timeseries prediction and would have good application prospects. However, existingKRLS algorithm, due to poor adaptive capability on dynamic environments,couldn’t meet the needs of online prediction accuracy and efficiency. This paperaddresses these issues to develop research works. The research works include:First, we study the basic principle of KRLS algorithm and its online timeseries prediction method. For analyzing dictionary updating method which is coreproblem of online prediction based on KRLS, we compare the sparsification method,the sliding window method and the fixed budget method. By comparingexperimental results of these three methods, the effects on prediction accuracy andefficiency are analyzed.Secondly, the prediction efficiency of Sparse KRLS algorithm which usessparsification method is high, but its adaptability is poor, so that the accuracy is low.For this problem, the Dynamic Forgetting Sparse KRLS algorithm is developed. Byintroducing a forgetting factor and then dynamic adapting the forgetting factor, thealgorithm improves the prediction accuracy. The experimental results show that,compared with the Sparse KRLS, the Dynamic Forgetting Sparse KRLS greatlyenhances the degree of prediction accuracy, but has little effect on the predictionefficiency.In addition, the Extended KRLS algorithm has state tracking capability, but itsprediction efficiency is very low and the prediction accuracy is also not satisfactory.For this problem, the Dynamic Forgetting Sparse Extended KRLS algorithm isproposed. By introducing sparsification method, the prediction efficiency isimproved and the problem of over fitting is solved. Then the dynamic forgettingmethod further improves its adaptive capacity, so that the higher predictionaccuracy is achieved. The experimental results show that, compared with theExtended KRLS, the Dynamic Forgetting Sparse Extended KRLS advances both of the prediction efficiency and accuracy significantly.Finally, the Dynamic Forgetting Sparse KRLS algorithm and the DynamicForgetting Sparse Extended KRLS algorithm are applied to NASA li-ion batterycapacity data and Heilongjiang mobile traffic data online prediction. The predictionresults show that, compared with classical KRLS-Tracker algorithm, the twoalgorithms which are proposed in this paper have advantages on both of theaccuracy and efficiency, and therefore they are more suitable for online prediction.Wherein the Dynamic Forgetting Sparse KRLS is more suitable for onlineprediction problem which has higher efficiency requirement and DynamicForgetting Sparse Extended KRLS is for higher accuracy requirement. |
