Chebyshev Polynomial Broad Learning System

Abstract

The broad learning system (BLS) has been attracting more and more attention due to its excellent property in the field of machine learning. A great deal of variants and hybrid structures of BLS have also been designed and developed for better performance in some specialized tasks. In this paper, the Chebyshev polynomials are introduced into the BLS to take advantage of their powerful approximation capability, where the feature windows are replaced by a set of Chebyshev polynomials. This new variant, named Chebyshev polynomial BLS (CPBLS), has a light structure with a reduction in computational complexity since the sparse autoencoder is removed. Instead, the dimension of each input sample is expended by n + 1 Chebyshev polynomials, mapping the original feature into a new feature space with higher dimension, which helps to classify the patterns in training. The proposed CPBLS is evaluated by some popular datasets from UCI and KEEL repositories, and it outperforms some representative neural networks and neuro-fuzzy models in terms of classification accuracy. The CPBLS also show some advantages over the recent developed compact fuzzy BLS (CFBLS) which indicates its great potential in future research and real-world applications.