Recursive clustering based on a Gustafson–Kessel algorithm

Abstract

In this paper an on-line fuzzy identification of Takagi Sugeno fuzzy model is presented. The presented method combines a recursive Gustafson-Kessel clustering algorithm and the fuzzy recursive least squares method. The on-line Gustafson-Kessel clustering method is derived. The recursive equations for fuzzy covariance matrix, its inverse and cluster centers are given. The use of the method is presented on two examples. First example demonstrates the use of the method for monitoring of the waste water treatment process and in the second example the method is used to develop an adaptive fuzzy predictive functional controller for a pH process. The results for the Mackey-Glass time series prediction are also given.

Evolving Takagi–Sugeno model based on online Gustafson-Kessel algorithm and kernel recursive least square method

“…Moreover, an extension of GK algorithm for evolving data stream was proposed in (Georgieva and Filev 2009) which applied Kohonen rule to update cluster centers and fuzzy covariance matrix. In this paper, we propose online GK that updates its parameter similar to (Dovžan and Škrjanc 2011), but number of clusters is changed over time by adding new clusters and merging similar clusters.…”

Automotive Applications of Evolving Takagi-Sugeno-Kang Fuzzy Models

“…The main property of the evolving Takagi-Sugeno-Kang fuzzy models, which gives them advantages over other fuzzy ones, consists in computing the rule bases by a learning process, that is, by continuous online rule base learning as shown in the classical and recent papers exemplified by [1][2][3][4][5][6][7][8][9][10]. The Takagi-Sugeno-Kang fuzzy models are obtained by evolving the model structure and parameters in terms of online identification algorithms.…”

Evolving principal component clustering with a low run-time complexity for LRF data mapping

“…Similarly, a generalized fuzzy C-means clustering is proposed by [17]. A recursive clustering and fuzzy Takagi Sugeno identification is presented in [18][19][20]. Fuzzy approaches can also be applied to identify a low size feature subset which maximize information and minimize data redundancy as in [29].…”