11. Interval Approach for Evolving Granular System Modeling

Physical systems change over time and usually produce considerable amount of nonstationary data. Evolving modeling of time-varying systems requires adaptive and flexible procedures to deal with heterogeneous data. Granular computing provides a rich framework for modeling time-varying systems using nonstationary granular data streams. This work considers interval granular objects to accommodate essential information from data streams and simplify complex real-world problems. We briefly discuss a new class of problems emerging in data stream mining where data may be either singular or granular. Particularly, we emphasize interval data and interval modeling framework. Interval-based evolving modeling (IBeM) approach recursively adapts both parameters and structure of rule-based models. IBeM uses ∪-closure granular structures to approximate functions. In general, approximand functions can be time series, decision boundaries between classes, control, or regression functions. Essentially, IBeM accesses data sequentially and discards previous examples; incoming data may trigger structural adaptation of models. The IBeM learning algorithm evolves and updates rules quickly to track system and environment changes. Experiments using heterogeneous streams of meteorological and financial data are performed to show the usefulness of the IBeM approach in actual scenarios.