  The random vector functional link (RVFL) network is well-regarded for its
strong generalization capabilities in the field of machine learning. However,
its inherent dependencies on the square loss function make it susceptible to
noise and outliers. Furthermore, the calculation of RVFL's unknown parameters
necessitates matrix inversion of the entire training sample, which constrains
its scalability. To address these challenges, we propose the Wave-RVFL, an RVFL
model incorporating the wave loss function. We formulate and solve the proposed
optimization problem of the Wave-RVFL using the adaptive moment estimation
(Adam) algorithm in a way that successfully eliminates the requirement for
matrix inversion and significantly enhances scalability. The Wave-RVFL exhibits
robustness against noise and outliers by preventing over-penalization of
deviations, thereby maintaining a balanced approach to managing noise and
outliers. The proposed Wave-RVFL model is evaluated on multiple UCI datasets,
both with and without the addition of noise and outliers, across various
domains and sizes. Empirical results affirm the superior performance and
robustness of the Wave-RVFL compared to baseline models, establishing it as a
highly effective and scalable classification solution.
