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The growing importance of time series information measure raises questions about how to effectively cluster a large number of nonlinear complex time series data and accurately extract more hidden information from them. In this paper, a clustering measurement and classification method for complex time series, the symmetrical exponential Tsallis relative information (SETRI) measure, is proposed, which aims to address these problems. The intrinsic characteristics of different types of time series information could be validly identified by this method. The modified multidimensional scaling (MDS) method, based on the SETRI measure, has the ability to display the data in the form of graphs for intuitive exhibition and accomplish the process of dimension reduction. The introduction of weighted permutation patterns allows a higher-accuracy classification not only for the time series dissimilarity quantification, but also for avoiding dispensable errors. Besides, the feasibility of the modified MDS classification method is visually and quantitatively verified by the simulated and real-world data. Compared with other MDS methods, the proposed method has better performance, which is reflected in the validity and rationality of the clustering results, thus further verifying the feasibility of the proposed method. Therefore, the new results will be helpful to develop complex data clustering and dimensionality reduction methods. [ABSTRACT FROM AUTHOR]

With the explosive growth of data quantity and rapid development of nonlinear dynamics as well as the growing demand for complex data classification in the field of artificial intelligence and machine learning, the research of complex time series, generated by complex systems, has attracted enormous interests. However, how to simultaneously distinguish different types of time series data and extract more accurate and detailed information from them in the light of localized and global scale perspectives remains significant and needs to be tackled. Thus, in this paper, we propose the fractional DisEn–Fisher plane, which is innovatively constructed by the fractional form of dispersion entropy and Fisher information measure. These are both effective tools to diagnose the essential properties of complex time series, to analyze the complexity of systems and to depict the contained statistical information with higher accuracy and effectiveness. Several classical entropy plane methods are selected as a comparison to design simulation experiments by simulated data and three real-world datasets. Comparative experimental results show that this method is a feasible and reliable improvement method, which will help to provide more additional information in time series recognition and dynamic characterization. It may not only provide new insights for further improvement of complex time series analysis, but also have important implications for developing complex data clustering methods. [ABSTRACT FROM AUTHOR]