The Development of Incremental Models

In this study, we introduce and discuss a concept of an incremental granular model. In contrast to typical rule-based systems encountered in fuzzy modeling, the underlying principle exploited here is to consider a two-phase development of fuzzy models. First, we build a standard regression model which could be treated as a preliminary construct capturing the linear part of the data and in this way forming a backbone of the entire construct. Next, all modeling discrepancies are compensated by a collection of rules that become attached to the regions of the input space where the error is localized. The incremental model is constructed by building a collection of information granules through some specialized fuzzy clustering, called context-based (conditional) fuzzy C-means that is guided by the distribution of error of the linear part of the model. The architecture of the model is discussed along with the major algorithmic phases of its development. In particular, the issue of granularity of fuzzy sets of context and induced clusters is discussed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vis-a-vis</i> the performance of the model. Numeric studies concern some low-dimensional synthetic data and several datasets coming from the machine learning repository.