Granular modelling of signals: A framework of Granular Computing

In spite of the evident diversity of models of signals and time series, there is still an urgent need to develop constructs that are both accurate and highly interpretable (human-centric). While a great deal of research has been devoted to the design of nonlinear models of time series (with anticipation of achieving high accuracy of prediction), an issue of interpretability (transparency) of the models remains an evident and ongoing challenge. The user-friendliness of models of time series comes hand in hand with an ability of humans to perceive and process abstract entities rather than plain numeric entities. With this regard, information granules and Granular Computing play an essential role. The use of information granules gives rise to a concept of granular models of time series or granular models of signals and time series, in brief. A granular interpretation of temporal data, where the role of information granularity is of paramount interest and effectively supports a human-centric description of relationships existing within data. This study revisits generic concepts of information granules and Granular Computing in this setting 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. The granular representation of time series is then discussed with a number of representation alternatives. A question of forming adjustable temporal slices (time windows) using which information granules are formed is discussed. With this regard presented is an optimization criterion of a sum of volumes of information granules whose minimization is realized through some methods of evolutionary or population-based optimization techniques. A series of illustrative examples is also discussed.

► A concept of granular models of signals of time series is proposed.
► Granular models are aimed at human-centric analysis of signals.
► Design of information granules are discussed with the use of sets and fuzzy sets.
► The principle of justifiable granularity shows how information granules are formed.
► Detailed algorithm of design of granular time series is presented.