Kernel risk-sensitive mean p-power loss based hyper-graph regularized robust extreme learning machine and its semi-supervised extension for sample classification

Extreme learning machine (ELM) has fast learning speed and perfect performance, at the same time, ELM provides a unified learning framework with a widespread type of feature mappings which can be applied in multiclass classification applications directly. These advantages make ELM become one of the best classification algorithms, and ELM has attracted great attention in supervised learning and semi-supervised learning. However, noise and outliers of data are usually existed in the real world, which will affect the performance of ELM. To improve the robustness and classification performance of ELM, we propose the Kernel Risk-Sensitive Mean p-power Loss Based Hyper-graph Regularized Robust Extreme Learning Machine (KRP-HRELM) method. On the one side, as a nonlinear similarity measure defined in the reproducing kernel space, the kernel risk-sensitive mean p-power loss (KRP) can effectively weaken the negative effects caused by noise and outliers. Therefore, the KRP is introduced into ELM to enhance its robustness. Then, the application of hyper-graph can help the ELM to explore higher-order geometric structures among more sampling points, thereby obtaining more comprehensive data information. In addition, to obtain a more sparsity network model, the L_2,1-norm is used to constrain the output weight. On the other side, improving the practical application ability of KRP-HRELM is also the focus of our research, so KRP-HRELM is extended to semi-supervised learning, which is called the semi-supervised KRP-HRELM (SS-KRP-HRELM). Notably, the results of the robustness experiment have proved that our method has extraordinary robustness. At the same time, by using four evaluation measures such as accuracy, recall, precision, and F1-measure, to evaluate the classification results, we can find that our method has obtained better classification performance than other advanced methods.