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Density-based semi-supervised online sequential extreme learning machine

  • Hybrid Artificial Intelligence and Machine Learning Technologies
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Abstract

This paper proposes a density-based semi-supervised online sequential extreme learning machine (D-SOS-ELM). The proposed method can realize online learning of unlabeled samples chunk by chunk. Local density and distance are used to measure the similarity of patterns, and the patterns with high confidence are selected by the ‘follow’ strategy for online learning, which can improve the accuracy of learning. Through continuous patterns selection, the proposed method ultimately achieves effective learning of unlabeled patterns. Furthermore, using local density and relative distance can effectively respond to the relationship between patterns. Compared with the traditional distance-based similarity measure, the ability to deal with complex data is improved. Empirical study on several standard benchmark data sets demonstrates that the proposed D-SOS-ELM model outperforms state-of-art methods in terms of accuracy.

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Notes

  1. The cutoff kernel can also be used for density description, but this method can lead to the same density of many points, which brings difficulties to subsequent operations. (cutoff kernel: \(\rho _i=\sum \nolimits _{j\in I_s\backslash {i}}\chi (d_{ij}-d_c)\), where \(\chi (x)=1\) if \(x<0\), else \(\chi (x)=0).\)

  2. As a rule of thumb, one can choose \(d_c\) so that the average number of neighbors is around 1% to 2% of the total number of points in the data set. If \(d_c\) is too large, the density of each data will be so large that the discrimination is not high. If the value is too small, then one category may be split into multiples, and the extreme case is that each of the data is a separate class. Locking the range at 1–2% is the empirical value of Rodriguez’s work based on several data sets and multiple trials.

  3. Rodriguez’s work suggests that in density clustering, a pattern X should belong to the same class as the pattern closest to the pattern X and with a larger density than pattern X.

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Acknowledgements

This work is supported in part by, the National Natural Science Foundation of PR China (61773219, 61503192), Natural Science Foundation of Jiangsu Province (BK20161533), and Qing Lan Project of Jiangsu Province.

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Authors and Affiliations

  1. Collaborative Innovation Center on Atmospheric Environment and Equipment Technology, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Min Xia

  2. Jiangsu Key Laboratory of Big Data Analysis Technology, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Min Xia, Jie Wang, Jia Liu & Liguo Weng

  3. College of Information Science and Technology, Nanjing Forestry University, Nanjing, 210037, China

    Yiqing Xu

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  1. Min Xia
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  2. Jie Wang
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  3. Jia Liu
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  4. Liguo Weng
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Correspondence to Min Xia.

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Xia, M., Wang, J., Liu, J. et al. Density-based semi-supervised online sequential extreme learning machine. Neural Comput & Applic 32, 7747–7758 (2020). https://doi.org/10.1007/s00521-019-04066-3

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