Abstract
In spite of the truly remarkable diversity of models of time series, there is still an evident need to develop constructs whose accuracy and interpretability are carefully identified and reconciled subsequently leading to highly interpretable (human-centric) constructs. While a great deal of research has been devoted to the design of nonlinear numeric models of time series (with an evident objective to achieve high accuracy of prediction), an issue of interpretability (transparency) of models of time series becomes an evident and ongoing challenge. The user-friendliness of models of time series comes with an ability of humans to perceive and process abstract constructs rather than dealing with plain numeric entities. In perception of time series, information granules (which are regarded as realizations of interpretable entities) play a pivotal role. This gives rise to a concept of granular models of time series or granular time series, in brief. This study revisits generic concepts of information granules and elaborates on a fundamental way of forming information granules (both sets--intervals as well as fuzzy sets) through applying a principle of justifiable granularity encountered in granular computing. Information granules are discussed with regard to the granulation of time series in a certain predefined representation space (viz. a feature space) and granulation carried out in time. The granular representation and description of time series is then presented. We elaborate on the fundamental hierarchically organized layers of processing supporting the development and interpretation of granular time series, namely (a) formation of granular descriptors used in their visualization, (b) construction of linguistic descriptors used afterwards in the generation of (c) linguistic description of time series. The layer of the linguistic prediction models of time series exploiting the linguistic descriptors is outlined as well. A number of examples are offered throughout the entire paper with intent to illustrate the main functionalities of the essential layers of the granular models of time series.
Highlights
Time series is a sequence of real-data, with each element in this sequence representing a value recorded at some time moment
We have proposed the concept of granular models of time series and elaborated on the ensuing descriptions of the temporal data carried out at the level of information granules
The first one, based on justifiable information granules is oriented towards supporting a graphic vehicle visualizing the nature of time series through a sequence of information granules reported in successive time windows
Summary
Time series is a sequence of real-data, with each element in this sequence representing a value recorded at some time moment. Current research in time series mining, time series characterization, and prediction comes with a visible diversity and richness of the conceptual and algorithmic pursuits In spite of their diversity, there is some evident and striking similarity; all of these approaches dwell upon the use and processing being realized at a numeric level. The granularity of information is an important facet being imperative to any offering of well-supported mechanisms of comprehension of the underlying temporal phenomenon In all these pursuits, information granules manifest along the two main dimensions (as noted above). Let us emphasize that information granules are sought as entities composed of elements being drawn together on a basis of similarity, functional closeness or spatial neighborhood The quality of such granulation (abstraction) of data is clearly related to the ability of this abstraction process to retain the essence of the original data (problem) while removing (hiding) all unnecessary details. It is emphasized that the introduced layered approach is suitable to deal with a variety of formalisms of information granules as well as the proposed constructs (such as e.g., the principle of justifiable granularity supporting a formation of a variety of information granules) and the notion of granular time series becomes well justified
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