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Robust regularized extreme learning machine with asymmetric Huber loss function

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Abstract

Sediment transport is one of the major challenging fields in hydrology. The tropical atmosphere, complex topography and occasional extreme precipitation are the fundamental explanations behind this challenge. Thus, the rivers in this situation contain a huge quantity of sediment, which may affect the river hydraulics. Hence, it is required to collect various parameters such as discharge, velocity, rainfall and sediment concentration to analyze the impact of sediment for river engineering practices and management. Therefore, the dataset which is collected from the river may contain outliers and noises. For improving the prediction accuracy of sediment load, we present robust regularized extreme learning machine frameworks to reduce the effect of noise by using the asymmetric Huber loss function named as AHELM and \( \varepsilon {-} \)insensitive Huber loss function named as \( \varepsilon {-} \)AHELM. Further, the problems are rewritten in the form of strongly convex minimization problems whose solutions are acquired by simple function iterative schemes. To ensure the effectiveness of the proposed approach, we have considered the real-world datasets with two types of noises. Furthermore, the proposed schemes are applied on real sediment load datasets (SLDs) which are collected from the Tawang Chu river of Arunachal Pradesh, India. The results reveal that proposed AHELM and \( \varepsilon {-} \)AHELM with multiquadric activation function are performed better for real-world datasets, whereas AHELM and \( \varepsilon {-} \)AHELM with sigmoid activation function perform efficiently and effectively for the sediment load prediction. In overall, the experimental results clearly exhibit the applicability as well as the usability of the proposed extreme learning machine with asymmetric Huber loss functions.

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Acknowledgement

This research was supported by ECRA, SERB, DST, New Delhi under early career research Award ECR/2016/001464. We will be forever grateful to NHPC LIMITED, TAWANG BASIN PROJECT for providing the SSL data.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, National Institute of Technology, Arunachal Pradesh, Yupia, 791112, India

    Deepak Gupta & Barenya Bikash Hazarika

  2. Department of Civil Engineering, National Institute of Technology, Arunachal Pradesh, Yupia, 791112, India

    Mohanadhas Berlin

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  1. Deepak Gupta
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  2. Barenya Bikash Hazarika
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  3. Mohanadhas Berlin
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Correspondence to Deepak Gupta.

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Gupta, D., Hazarika, B.B. & Berlin, M. Robust regularized extreme learning machine with asymmetric Huber loss function. Neural Comput & Applic 32, 12971–12998 (2020). https://doi.org/10.1007/s00521-020-04741-w

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