Data Informed Initialization of Fuzzy Membership Functions

Abstract Takagi-Sugeno-Kang fuzzy neural networks (TSKFNNs) are frequently utilized to model regression problems. One of the most important challenges with TSKFNNs relates to the optimization of the starting parameters. With better initialization of these parameters, it may be possible to improve the speed of model convergence by having a better starting point as well as minimizing the risk of the model fitting to the local minima. The starting parameters for TSK fuzzy systems, specifically the number of membership functions (MFs) per input domain and the shape of each MF, are typically informed by human experts. However, human insights may include bias or be challenging to acquire. In existing research, the shape and number of MFs are typically kept constant across all input features for simplicity. However, having a dynamic initialization of MFs may allow the TSKFNNs to more accurately capture valuable information the input feature space. Therefore, it is hypothesized that a data-driven initialization algorithm may overcome such challenges when developing TSKFNNs. This paper presents a novel approach using parameter-free clustering and Akaike Information Criterion to the initialization of MFs for TSKFNNs. The effectiveness of the proposed method is validated with nine popular datasets and benchmarked against the state-of-the-art TSK fuzzy systems. The experimental results demonstrate that the proposed data-informed method achieves superior generalization performance in testing compared to the benchmark model. The proposed model Fixed-N-Flexi-S with a personalized number of MFs can reduce root mean square error by over $$10\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>10</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> compared with the baseline model FWF-NA on 7 out of 9 datasets. The proposed model Fixed-N-Flexi-S with multiple sorts of MF shapes can reduce root mean square error by more than $$9\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>9</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> compared with the baseline model FWF-NA on 4 out of 9 datasets.