Robust DTW-based entropy fuzzy clustering of time series
提出一种基于熵正则化的鲁棒模糊C-中心点方法，通过动态时间弯曲处理不同长度时间序列，能有效应对异常值和噪声，并识别切换行为，在罗马空气污染物数据中验证了其有效性。
Abstract Time series are complex data objects whose partitioning into homogeneous groups is still a challenging task, especially in the presence of outliers or noisy data. To address the problem of robustness against outliers in clustering techniques, this paper proposes a robust fuzzy C-medoids method based on entropy regularization. In-depth, we use an appropriate exponential transformation of the dissimilarity based on Dynamic Time Warping, which can be computed also for time series of different length. In addition, the fuzzy framework provides the necessary flexibility to cope with the complexity of the features space. It allows a time series to be assigned to more than one group, considering potential switching behaviours. Moreover, the use of a medoids-based approach enables the identification of observed representative objects within the dataset, thus enhancing interpretability for practical applications. Through an extensive simulation study, we successfully demonstrate the effectiveness of our proposal, comparing and emphasizing its strengths. Finally, our proposed methodology is applied to the daily mean concentrations of three air pollutants in 2022 in the Province of Rome. This application highlights its potential, namely the capability to intercept outliers and switching time series while preserving group structures.