Modeling of prediction system: An application of the nearest neighbor approach to chaotic data

Abstract

This paper is about modeling of chaotic systems via nearest neighbor approach. This approach holds the principle that future data can be predicted using past data information. Here, all the past data known as neighbors. There are various prediction models that have been developed through this approach. In this paper, the zeroth-order approximation method (ZOAM) and improved ZOAM, namely the k-nearest neighbor approximation (KNNAM) and weighted distance approximation method (WDAM) were used. In ZOAM, only one nearest neighbor is used to predict future data while KNNAM uses more than one nearest neighbor and WDAM add the distance element for prediction process. These models were used to predict one of the chaotic data, Logistic map. 3008 Logistic map data has been produced, in which the first 3000 data were used to train the model while the rest is used to test the performance of the model. Correlation coefficient and average absolute error are used to view the performance of the model. The prediction results by the three models are in excellent agreement with the real data. This shows that the nearest neighbor approach works well to predict the chaotic data. Unfortunately, increasing the number of nearest neighbors from ZOAM to KNNAM not managed to improve prediction performance. However, the added element of the distance is a great idea for improving prediction performance. Overall, WDAM is the best model to predict the chaotic data compared to ZOAM and KNNAM.