Granular description of data in a non-stationary environment

Abstract

When developing models of non-stationary data, it becomes imperative to endow them with some meaningful update mechanisms, viz to provide with sufficient capabilities to accommodate changing characteristics of the environment. These mechanisms make the models of data evolvable. In the study, we introduce and discuss a class of evolvable models of data with the main objective to describe and interpret the incoming data. We advocate that information granularity and ensuing information granules are central to the characterization and interpretation of the dynamics and variability of numeric data. The relevance of information granules describing the data is evaluated in their abilities to construct the associated Takagi–Sugeno rule-based models. It is shown how the condition part of the rules formed by information granules changes when exposed to data of varying characteristics. Along with the structural facet of evolvability discussed is its parametric manifestation present in terms of the changes (updates) of the parameters of the local models standing in the conclusion part of the rules. The continuity of the evolving information granules (being crucial to their interpretability) is assured by running the clustering scheme initialized on the basis of the previously formed clusters (conditions of the rules) rather than starting FCM from some random configuration. We introduce some graph-oriented visualization means to provide a concise insight into the dynamics of information granules. As an interesting alternative, we introduce a granular fuzzy model where the added granularity of the parameters of a stationary fuzzy model is considered as a way to compensate for the non-stationary of the described system. A series of experiments is reported on with intent to demonstrate the performance of the model, analyze mechanisms of evolution of information granules, and deliver some useful comparative analysis.