A non-linear clustering method for fuzzy time series: Histogram damping partition under the optimized cluster paradox

The clustering problem is an emergent issue in fuzzy time series.The existing clustering methods deal with the number of clusters or their size.Optimized cluster paradox refers to that trade-off between size and number.The histogram damping algorithm (HDP) is proposed to deal with this problem by estimating a proper cluster form with number and size characteristics.The proposed model is tested against the conventional methods and the case of random data is also presented. Results indicated superiority of the proposed method. The aim of this paper is to investigate the problem of finding the efficient number of clusters in fuzzy time series. The clustering process has been discussed in the existing literature, and a number of methods have been suggested. These methods have several drawbacks, especially the lack of cluster shape and quantity optimization. There are two critical dimensions in a fuzzy time series clustering: the selection of a proper interval for fuzzy clusters and the optimization of the membership degrees among the fuzzy cluster set. The existing methods for the interval selection assume that the intended data has a short-tailed distribution, and the cluster intervals are established in identical lengths (e.g. Song and Chissom, 1994; Chen, 1996; Yolcu et al., 2009). However, the time series data (particularly in economic research) is rarely short-tailed and mostly converges to long-tail distribution because of the boom-bust market behavior. This paper proposes a novel clustering method named histogram damping partition (HDP) to define sub-clusters on the standard deviation intervals and truncate the histogram of the data by a constraint based on the coefficient of variation. The HDP approach can be used for many different kinds of fuzzy time series models at the clustering stage.

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