Resolving Global and Local Drifts in Data Stream Regression using Evolving Rule-Based Models

In this paper, we present new concepts for dealing with drifts in data streams during the run of on-line modeling processes for regression problems in the context of evolving fuzzy systems. Opposed to the nominal case based on conventional life-long learning, drifts are requiring a specific treatment for the modeling phase, as they refer to changes in the underlying data distribution or target concepts, which makes older learned concepts obsolete. Our approach comes with three new stages for an appropriate drift handling: 1.) drifts are not only detected, but also quantified with a new extended version of the Page-Hinkley test, which overcomes some instabilities during downtrends of the indicator; 2.) based on the current intensity quantification of the drift, the necessary degree of forgetting (weak to strong) is extracted (adaptive forgetting); 3.) the latter is achieved by two variants, a.) a single forgetting factor value, accounting for global drifts, and b.) a forgetting factor vector with different entries for separate regions of the feature space, accounting for local drifts. Forgetting factors are integrated into the learning scheme of both, the antecedent and consequent parts of the evolving fuzzy systems. The new approach will be evaluated on high-dimensional data streams, where the results will show that 1.) our adaptive forgetting strategy outperforms the usage of fixed forgetting factors throughout the learning process and 2.) forgetting in local regions may improve forgetting in global ones when drifts appear locally.