Sparse Generalized Robust Stochastic Configuration Networks and Industrial Applications

In many real-world applications, the collected data with high dimensionality regularly also contain noise and outliers, which may result in learner model with insufficient generalization. The stochastic configuration network (SCN) is commonly applied to data analytics and achieve promising performance on industrial data modeling. However, the output weights of SCN are computed by the least-squares method, which is susceptible to noise and outliers. In this context, a novel framework of sparse generalized robust SCN (SGRSCN) is presented in this article. An arbitrary concave function is introduced in the loss function of SGRSCN that is employed to set the penalty weights for each training samples, which can reduce the negative impacts of noise and outliers to some extent. In addition, to address the architecture complexity and ill-posed problems of SCN when processing high-dimensional data, the loss function also consists of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${L}_{{2},{p}}$</tex-math></inline-formula>-norm (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol {0&lt; }{p}\boldsymbol {&lt; 1}$</tex-math></inline-formula>) regularization term. By adjusting <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i>, the sparse model can be obtained. Then, the alternating optimization algorithm is applied to the optimization of loss function and the convergence analysis of the optimization process is provided. Moreover, a typical concave function is selected as an example using the framework of SGRSCN. Finally, the performance of SGRSCN is evaluated on two benchmark datasets and a real-world dataset with high-dimensional features. The experimental results demonstrate the superiority of SGRSCN.