Wavelet kernel large margin distribution machine-based regression for modelling the river suspended sediment load

Abstract

Estimating the suspended sediment load (SSL) in rivers is among the key challenges in rivers. The major reason is that the daily river SSL data may contain non-linear components. Therefore, the traditional models face difficulty in handling the nonlinearity in the datasets. Very recently, a large margin distribution machine-based regression (LDMR) was proposed in the spirit of the large margin distribution machine (LDM). LDMR uses the Gaussian kernel for the selection of nonlinear kernels and tries to reduce the quadratic loss function and insensitive loss function concurrently. Wavelet kernels are very effective in approximating any arbitrary non-linear functions. To realize the benefit of wavelet kernel in LDMR, this paper suggests two novel wavelet kernel-based LDMR models as Morlet kernelized LDMR (MKLDMR) and Mexican hat kernelized LDMR (MHKLDMR) for river SSL estimation. The experiments were performed on a few SSL datasets which were gathered from the Tawang Chu River, India. Further, these models were also applied to a few artificially generated datasets and some real-world datasets. To validate the efficacy of MKLDMR and MHKLDMR, their generalization performance was collated with support vector regression (SVR), twin SVR (TSVR), random vector functional link without direct link (RVFLwoDL), iterative-based Lagrangian twin parametric insensitive SVR (ILTPISVR), robust support vector quantile regression (RSVQR), neuro fuzzy RVFL (NF-RVFL), ensemble deep RVFL (edRVFL) and LDMR. The experimental outcomes on the artificial datasets, real-world datasets and SSL datasets of the MKLDMR and MHKLDMR models imply the usability and effectiveness of the proposed models for SSL prediction.