Algorithm 1 The kernel-based ELM with regularization.

Input: training samples {(${\mathit{x}}_i$, ${\mathit{t}}_i$) |${\mathit{x}}_i\in {\mathbb{R}}^m$, ${\mathit{t}}_i\in {\mathbb{R}}^n$, $i=1,\cdots ,P$}; the regularization parameter C; the kernel function $K(\mathit{a},\mathit{b})$; the input of a random testing sample $\mathit{x}$.   (1) Calculate the kernel matrix ${\Omega }_{\mathrm{ELM}}$ of the given P training samples based on Equation (6);   (2) Calculate the output of the test sample $\mathit{O}$ based on Equation (8). Output: the test sample $\mathit{O}$.