Time Series Analysis And Modeling Method Research Based On Granular Computing

In the today's big data era, individual sample data is no longer focus of our attention and the understanding and cognition of data is far more important than individual sample data. Con-sidering that (1) the process of modeling overly depends on individual sample data, which re-sults in lack of interpretation; (2) the constructed models pursue to aim for accuracy on the numerical level, whereas it is not absolutely necessary in the environment of big data; (3) the output of constructed models is a single numerical data, which is very difficult to perceive by users in the environment of big data, the traditional modelling approaches of time series can not satisfy requirements already for actual application. As one of emerging and fastest-growing information-processing paradigms in the domain of computational intelligence, granular com-puting uncovers granulation cognition mechanism for human to process complex information. It can form a united and coherent platform of constructing, describing, and processing information granules by incorporating the existing technologies and formalisms of sets (interval analysis), fuzzy sets, rough sets, shadowed sets, probabilistic sets and alike, which results in birth of new theories and methods of computational intelligence. In this background, starting with miming granulation cognition mechanism for human to process complex information, this paper inves-tigates three key problems (that is the sound information granulation of time series. the analysis and interpretation of time series based on information granulation and the modeling of time series based on information granulation) from the analysis and modeling of time series on the basis of granular computing by using fuzzy set theory and fuzzy modeling methods for reference. Main research results obtained are as follows:Firstly, the multi-granularity interval information granulation method of time series is pro-posed for the problem that information granules constructed by traditional granulation methods can not capture nature of data in the process of the sound information granulation of time series. In the proposed method, the problem of sound information granulation of data presented on time windows of time series is converted to the optimization problem of bounds of interval infor-mation granules with constraint of variable ??[0.1] by introducing the reasonability concept and the specificity concept of information granules under interval formalism, where variable ? represents the level of information granularity used in the process of granulating data on corre-sponding time window of time series. By solving the optimization problem with different values of ? to introduce interval information granules under the corresponding granularity level of ?, multi-granularity interval information granulation of data which are presented on the same time window of time series can be realized. A series of interval information granules with nested structure are produced by using the proposed granulation method to granulate data. They can be regarded as a whole and called the nested interval information granule. It represents results of interval information granulation for data presented on the corresponding time window of time series under the different level of information granularity.Secondly, the clustering method of the nested rectangle information granules with nested rectangle structure in the granular feature space is proposed for analysis and interpretation of time series based on information granulation. Uncovering in the granular feature space the structure and representation of the nested rectangle information granules which can be constructed by using multi-granularity interval information granulation method to respectively granulate am-plitude signal and its first order difference of time series from view of geometry, the proposed clustering method exploit the decomposability and the synthesizability of the nested rectangle information granule to cluster the nested rectangle information granules associated with time window in the granular feature space by using fuzzy C-means clustering algorithm for refer-ence. Furthermore, the granular prototypes formed on the granular feature space imply seman-tics which are used to describe dynamic feature of data presented on the corresponding time window of time series, and thus the analysis and interpretation of time series can be realized by calculating matching degree between the nested rectangle information granule formed on the corresponding time window of time series and these granular prototypes in the granular feature space. The experiments on several time series datasets show on the results obtained by using the proposed method to analyze and interpret time series agree with human's cognition.Thirdly, the layered method of time series modeling based on multi-granularity interval in-formation granulation and two performance evaluation index of time series granular model are proposed to realize granulation modeling of time series. Considered on amplitude signal and its first order difference of time series, the proposed granulation modeling method of time series starts with granulation cognition mechanism for human to process complex information prob-lems. It can compress scale of time series and transforms the original time series to the gran-ular time series by multi-granularity interval information granulation, and incorporate domain knowledge into the granulation modeling process by capturing dynamic semantics feature using to describe data presented on the corresponding time window of time series which can be ob-tained by clustering the nested rectangle information granules in the granular feature space, and mine dynamic causality among the nested rectangle information granules associated with time window in the granular feature space to construct the granular model of time series. The related experimental results show that the fuzzy cognitive map time series granular model constructed according to the proposed method has better interpretability, and its output is an information granule (interval) with semantics, which can reflect holistic dynamic characteristics (semantics) and change range of data (interval) on the corresponding time window of time series. In this way the output of constructed granular model can be easily interpreted and perceived by users and provides effective support for users to make decision reasonably.