Robust Classification via Interval Type-2 Fuzzy C-Means and Gradient Boosting

Abstract

This article introduces the Bayesian probabilistic fuzzy neural network (BPFNN), designed to overcome the limitations of Fuzzy C-Means (FCM) clustering, which struggles with uncertainty, noise, nonlinearity, and interpretability. Additionally, it addresses the shortcomings of traditional objective functions, such as mean squared error (MSE), which fail to capture the complexities inherent in high-dimensional and uncertain datasets. The BPFNN framework integrates Bayesian probabilistic modeling with advanced fuzzy clustering techniques, utilizing a non-Gaussian probability density function to better represent data uncertainties. A hybrid Markov chain Monte Carlo strategy, combining Metropolis-Hastings for membership updates and Gibbs sampling for cluster parameter estimation, is employed to effectively model uncertainty. For the learning of connection weights, the generalized cross-entropy loss function is applied, and the iteratively reweighted least squares algorithm is used to update the weights, allowing for a more precise quantification of the divergence between predicted and ground truth labels. Experimental evaluations on several benchmark datasets, as well as a high-dimensional laser-induced breakdown spectroscopy (LIBS) spectral dataset, demonstrate that the proposed BPFNN significantly outperforms both traditional methods and State-of-the-Art techniques in terms of classification accuracy and robustness. Notably, BPFNN achieves an average accuracy improvement of 3.2% over conventional models on benchmark datasets, with a 5.3% improvement on the LIBS dataset, highlighting its substantial advancement in the field.