Background As a machine learning method with high performance and excellent generalization ability, extreme learning machine (ELM) is gaining popularity in various studies. Various ELM-based methods for different fields have been proposed. However, the robustness to noise and outliers is always the main problem affecting the performance of ELM. Results In this paper, an integrated method named correntropy induced loss based sparse robust graph regularized extreme learning machine (CSRGELM) is proposed. The introduction of correntropy induced loss improves the robustness of ELM and weakens the negative effects of noise and outliers. By using the L2,1-norm to constrain the output weight matrix, we tend to obtain a sparse output weight matrix to construct a simpler single hidden layer feedforward neural network model. By introducing the graph regularization to preserve the local structural information of the data, the classification performance of the new method is further improved. Besides, we design an iterative optimization method based on the idea of half quadratic optimization to solve the non-convex problem of CSRGELM. Conclusions The classification results on the benchmark dataset show that CSRGELM can obtain better classification results compared with other methods. More importantly, we also apply the new method to the classification problems of cancer samples and get a good classification effect.

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