Adaptive Fuzzy Filtering in a Deterministic Setting
Manyreal-world applications involve the filtering and estimation of process variables. This study considers the use of interpretable Sugeno-type fuzzy models for adaptive filtering. Our aim in this study is to provide different adaptive fuzzy filtering algorithms in a deterministic setting. The algorithms are derived and studied in a unified way without making any assumptions on the nature of signals (i.e., process variables). The study extends, in a common framework, the adaptive filtering algorithms (usually studied in signal processing literature) and p- norm algorithms (usually studied in machine learning literature) to semilinear fuzzy models. A mathematical framework is provided that allows the development and an analysis of the adaptive fuzzy filtering algorithms. We study a class of nonlinear LMS-like algorithms for the online estimation of fuzzy model parameters. A generalization of the algorithms to the p- norm is provided using Bregman divergences (a standard tool for online machine learning algorithms).
adaptive filtering algorithms bregman divergences p-norm robustness sugeno fuzzy models