Application of improved chaotic method in determining number of k-nearest neighbor for CO data series

Abstract

This study is designed to i) apply chaotic approach in predicting Carbon Monoxide (CO) data series and ii) improve the method in determining number of k–nearest neighbor. Chaotic approach is one alternative approach to predict any data series. Prediction through chaotic approach is made after three important parameters which are delay time τ, embedding dimension m and numbers of nearest neighbor k were determined. Therefore, the chaotic approach is applied. In this study, predictions are done to Carbon Monoxide time series observed at Shah Alam in Malaysia. Parameters τ and m are determined through average mutual information and Cao method respectively. While for k, most of the past researches frequently used try and error method. In this study an improvement of the method in determining the number of k is introduced. This improved method is done through plotting the graph of k versus the correlation coefficient (cc) of prediction model. Parameter cc is obtained through the prediction of data series using local mean approximation method (LMAM), local linear approximation method (LLAM) and improved local linear approximation method (ILLAM). Result shows that the cc value of LMAM is 0.9821 with k = 7, LLAM is 0.9873 with k = 3 and ILLAM is 0.9913 with k = 13. Therefore, the improved methods suggest that the optimal value of k is ranged from 3 ≤ k ≤ 13. It is hoped that the improved method can be used for future research in developing a better prediction model for chaotic data series.