Hierarchical clustering of ensemble prediction using LOOCV predictable horizon for chaotic time series

Recently, we have presented a method of ensemble prediction of chaotic time series. The method employs strong learners capable of making predictions with small error, where usual ensemble mean does not work well owing to the long term unpredictability of chaotic time series. Thus, we have developed a method to select a representative prediction from a set of plausible predictions by means of using LOOCV (leave-one-out cross-validation) measure to estimate predictable horizon. Although we have shown the effectiveness of the method, it sometimes fails to select the representative prediction with long predictable horizon. In order to cope with this problem, this paper presents a method to select multiple candidates of representative prediction by means of employing hierarchical K-means clustering with K = 2. From numerical experiments, we show the effectiveness of the method and an analysis of the property of LOOCV predictable horizon.