Fuzzy clustering of time series based on trend feature information granulation

Clustering is a means to mine valuable information from complex and massive time series data sets, and information granulation is a new strategy to simulate human thinking and solve complex problems. The combination of the two provides a new perspective for knowledge discovery of time series. In this paper, the feature extraction of time series is carried out, and the trend feature is abstractly represented by information granulation to reduce the data scale. Then, a fuzzy C-means clustering algorithm of time series based on trend feature information granules is proposed. First, hodrick prescott (HP) filtering is used to process the raw time series data, removing noise and redundancy. Secondly, the global continuous fitting function is obtained by polynomial curve fitting (PCF) to the time series data. Thirdly, the polynomial function derivative (PFD) values of each time point are obtained by the function as the trend feature, and the time series is transformed into the trend feature series. Then, the feature sequence is segmented optimally. According to the principle of reasonable particle size, the feature sequence is represented by a group of information granule, and the dimensionality is reduced to transform the trend feature information granule (TFIG) sequence. Finally, the fuzzy clustering of time series is realized in the transformed representation space (information granule space). In the process of clustering, a trend feature information granule-based dynamic time warping (TFIG-DTW) algorithm is developed for calculating the distance of two equal-length or unequal-length granular time series, and weighted DTW barycenter averaging (wDBA) is extended to fuzzy C-means (FCM) algorithm to update cluster prototype. Finally, UCR time series database and stock data set are used as experimental objects to verify the effectiveness and superiority of fuzzy clustering method.