Boosting Sparsity in Gram Matrix of Fuzzy Regression Models through Radial Basis Functions

The sparsity of the Gram matrix in linear regression can influence the model's accuracy. Sparse matrices reduce computational complexity and improve generalization by minimizing overfitting. This advantage is particularly beneficial in high-dimensional data where the number of features exceeds the number of observations. This paper explores the integration of Radial Basis Functions (RBFs) in developing sparse Gram matrix fuzzy regression models. RBFs are powerful tools for function approximation, defined by their dependence on the distance from a center point, which allows for flexible modeling of nonlinear relationships. The focus will be on compactly supported RBF kernels, which facilitate sparsity in the Gram matrix, thereby improving computational efficiency and memory usage. By leveraging the properties of RBFs, particularly their ability to localize influence and reduce dimensionality, we aim to enhance the performance of fuzzy regression models. This study will present theoretical insights and empirical results demonstrating how the adoption of RBFs can lead to significant improvements in model accuracy and computational speed, making them a valuable asset in the field of fuzzy regression analysis.

کلیدواژه ها:

Fuzzy number ، Regression model ، Radial basis functions ، Kernel