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23-11-2020 | Original Article

# Hierarchical extreme learning machine with L21-norm loss and regularization

Journal:
International Journal of Machine Learning and Cybernetics
Authors:
Rui Li, Xiaodan Wang, Yafei Song, Lei Lei
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## Abstract

Recently, multilayer extreme learning machine (ELM) algorithms have been extensively studied for hierarchical abstract representation learning in the ELM community. In this paper, we investigate the specific combination of $$L_{21}$$-norm based loss function and regularization to improve the robustness and the sparsity of multilayer ELM. As we all known, the mean square error (MSE) cost function (or squared $$L_{2}$$-norm cost function) is commonly used as optimization cost function for ELM, but it is sensitive to outliers and impulsive noises that are pervasive in real-world data. Our $$L_{21}$$-norm loss function can lessen the harmful influence caused by noises and outliers and enhance robustness and stability of the learned model. Additionally, the row sparse inducing $$L_{21}$$-norm regularization can learn the most-relevant sparse representation and reduce the intrinsic complexity of the learning model. We propose a specific combination of $$L_{21}$$-norm loss function and regularization ELM auto-encoder (LR21-ELM-AE), and then stack LR21-ELM-AE hierarchically to construct the hierarchical extreme learning machine (H-LR21-ELM). Experiments conducted on several well-known benchmark datasets are presented, the results show that the proposed H-LR21-ELM can generate a more robust, more discriminative and sparser model compared with the other state-of-the-art multilayer ELM algorithms.

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