Clustering time series under trend-oriented fuzzy information granulation

Abstract

This paper proposes a trend-oriented time series granulation method to transform a long numerical time series into a relatively short granular time series which is consist of a group of unequal-size linear fuzzy information granules (LFIG). The transformed granular time series not only captures the main characteristics like trends and fluctuations of the original time series, but also saves the amount of calculation in time series clustering. Inspired by the distance measure of two equal-size LFIGs and the dynamic time warping, this paper also defines the distance measures for two unequal-size LFIGs and two LFIG time series. Based on such distance measures, the k-medoids method is employed to cluster the datasets coming from UCR time-series database. The clustering performance expressed in terms of computing time and the Rand Index demonstrates the effectiveness and advantages of the proposed time series granulation method and distance measurement. The main original aspects of this study concern the granular representation of time series with unequal-size granules, and the distance measurement of unequal-length granular time series.