An improved hybrid regularization approach for extreme learning machine

Extreme learning machine (ELM) is a network model that arbitrarily initializes the first hidden layer and can be computed speedily. In order to improve the classification performance of ELM, a ${\mathrm{\ell }}_2$ and ${\mathrm{\ell }}_{0.5}$ regularization ELM model (${\mathrm{\ell }}_2$-${\mathrm{\ell }}_{0.5}$-ELM) is proposed in this paper. An iterative optimization algorithm of the fixed point contraction mapping is applied to solve the ${\mathrm{\ell }}_2$-${\mathrm{\ell }}_{0.5}$-ELM model. The convergence and sparsity of the proposed method are discussed and analyzed under reasonable assumptions. The performance of the proposed ${\mathrm{\ell }}_2$-${\mathrm{\ell }}_{0.5}$-ELM method is compared with BP, SVM, ELM, ${\mathrm{\ell }}_{0.5}$-ELM, ${\mathrm{\ell }}_1$-ELM, ${\mathrm{\ell }}_2$-ELM and ${\mathrm{\ell }}_2$-${\mathrm{\ell }}_1$ELM, the results show that the prediction accuracy, sparsity, and stability of the ${\mathrm{\ell }}_2$-${\mathrm{\ell }}_{0.5}$-ELM are better than the other $7$ models.