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Imbalanced ELM Based on Normal Density Estimation for Binary-Class Classification

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Trends and Applications in Knowledge Discovery and Data Mining (PAKDD 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9794))

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Abstract

The imbalanced Extreme Learning Machine based on kernel density estimation (imELM-kde) is a latest classification algorithm for handling the imbalanced binary-class classification. By adjusting the real outputs of training data with intersection point of two probability density functions (p.d.f.s) corresponding to the predictive outputs of majority and minority classes, imELM-kde updates ELM which is trained based on the original training data and thus improves the performance of ELM-based imbalanced classifier. In this paper, we analyze the shortcomings of imELM-kde and then propose an improved version of imELM-kde. The Parzen window method used in imELM-kde leads to multiple intersection points between p.d.f.s of majority and minority classes. In addition, it is unreasonable to update the real outputs with intersection point, because the p.d.f.s are estimated based on the predictive outputs. Thus, in order to improve the shortcomings of imELM-kde, an imbalanced ELM based on normal density estimation (imELM-nde) is proposed in this paper. In imELM-nde, the p.d.f.s of predictive outputs corresponding to majority and minority classes are computed with normal density estimation and the intersection point is used to update the predictive outputs instead of real outputs. This makes the training of probability density estimation-based imbalanced ELM simpler and more feasible. The comparative results show that our proposed imELM-nde performs better than unweighted ELM and imELM-kde for imbalanced binary-class classification problem.

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Notes

  1. 1.

    For simplicity, we don’t use the ridge regression-based ELM [6] in this paper. All the probability density estimation-based ELMs discussed below are designed based on ELM without the regularization factor \(C>0\).

  2. 2.

    In [17], the authors didn’t provide the specific discussion regarding how to map the predictive outputs into a one-dimensional space. Here, we used the mapping method in our proposed inELM-nde to deal with this issue.

  3. 3.

    KEEL-dataset repository. http://www.keel.es/.

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Acknowledgments

This work is supported by China Postdoctoral Science Foundations (2015M572361 and 2016T90799), Basic Research Project of Knowledge Innovation Program in Shenzhen (JCYJ201503241400368 25), and National Natural Science Foundations of China (61503252, 61473194, 71371063, and 61473111).

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Authors and Affiliations

  1. College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, 518060, China

    Yulin He, Rana Aamir Raza Ashfaq, Joshua Zhexue Huang & Xizhao Wang

  2. Department of Computer Science, Bahauddin Zakariya University, Multan, Pakistan

    Rana Aamir Raza Ashfaq

Authors
  1. Yulin He
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  2. Rana Aamir Raza Ashfaq
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  3. Joshua Zhexue Huang
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  4. Xizhao Wang
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Corresponding author

Correspondence to Yulin He .

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Editors and Affiliations

  1. New Mexico State University , Las Cruces, New Mexico, USA

    Huiping Cao

  2. University of Technology Sydney , Sydney, New South Wales, Australia

    Jinyan Li

  3. Massey University , Auckland, New Zealand

    Ruili Wang

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He, Y., Ashfaq, R.A.R., Huang, J.Z., Wang, X. (2016). Imbalanced ELM Based on Normal Density Estimation for Binary-Class Classification. In: Cao, H., Li, J., Wang, R. (eds) Trends and Applications in Knowledge Discovery and Data Mining. PAKDD 2016. Lecture Notes in Computer Science(), vol 9794. Springer, Cham. https://doi.org/10.1007/978-3-319-42996-0_5

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  • DOI: https://doi.org/10.1007/978-3-319-42996-0_5

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