An Improved Virtual Sample Generation Method Based on Quadrat Density Method and Quantile Regression for Small Sample Size Problem

Qun Xiong Zhu; Meiyu Zhu; Yuan Xu; Yan Lin He

doi:10.1109/DDCLS52934.2021.9455489

An Improved Virtual Sample Generation Method Based on Quadrat Density Method and Quantile Regression for Small Sample Size Problem

Qun Xiong Zhu, Meiyu Zhu, Yuan Xu, Yan Lin He

Beijing University of Chemical Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The gradual realization of automation has caused explosive growth of data and increased the amount of researchable data. However, due to the low probability of occurrence and high difficulty in obtaining, representative data is lacking. One of the effective ways to solve this problem is virtual sample generation (VSG). In this study, a novel VSG method is put forward. The sample squares are divided in the input space according to Dominance Analysis, and the virtual inputs are generated by using the Quadrat Density Method in reverse. The corresponding virtual output is predicted by Gaussian Process Regression. Through Quantile Regression, analyze the correlation between input variables and output variables. The generated virtual samples are screened, and the virtual samples that do not meet the correlation relationship are eliminated. In order to verify the effectiveness of the proposed method, experiments are carried out on two numerical simulations and a real-world application from a cascade reaction process for high-density polyethylene. The results show that the method proposed in this paper is superior to other methods.

Original language	English
Title of host publication	Proceedings of 2021 IEEE 10th Data Driven Control and Learning Systems Conference, DDCLS 2021
Editors	Mingxuan Sun, Huaguang Zhang
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	854-859
Number of pages	6
ISBN (Electronic)	9781665424233
DOIs	https://doi.org/10.1109/DDCLS52934.2021.9455489
Publication status	Published - 14 May 2021
Externally published	Yes
Event	10th IEEE Data Driven Control and Learning Systems Conference, DDCLS 2021 - Suzhou, China Duration: 14 May 2021 → 16 May 2021

Publication series

Name	Proceedings of 2021 IEEE 10th Data Driven Control and Learning Systems Conference, DDCLS 2021

Conference

Conference	10th IEEE Data Driven Control and Learning Systems Conference, DDCLS 2021
Country/Territory	China
City	Suzhou
Period	14/05/21 → 16/05/21

Keywords

dominance analysis
quadrat density method
quantile regression
Small sample size problems
virtual sample generation

Access to Document

10.1109/DDCLS52934.2021.9455489

Cite this

Zhu, Q. X., Zhu, M., Xu, Y., & He, Y. L. (2021). An Improved Virtual Sample Generation Method Based on Quadrat Density Method and Quantile Regression for Small Sample Size Problem. In M. Sun, & H. Zhang (Eds.), Proceedings of 2021 IEEE 10th Data Driven Control and Learning Systems Conference, DDCLS 2021 (pp. 854-859). Article 9455489 (Proceedings of 2021 IEEE 10th Data Driven Control and Learning Systems Conference, DDCLS 2021). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/DDCLS52934.2021.9455489

Zhu, Qun Xiong ; Zhu, Meiyu ; Xu, Yuan et al. / An Improved Virtual Sample Generation Method Based on Quadrat Density Method and Quantile Regression for Small Sample Size Problem. Proceedings of 2021 IEEE 10th Data Driven Control and Learning Systems Conference, DDCLS 2021. editor / Mingxuan Sun ; Huaguang Zhang. Institute of Electrical and Electronics Engineers Inc., 2021. pp. 854-859 (Proceedings of 2021 IEEE 10th Data Driven Control and Learning Systems Conference, DDCLS 2021).

@inproceedings{118811a4ccba4d3facef02b26b364ef4,

title = "An Improved Virtual Sample Generation Method Based on Quadrat Density Method and Quantile Regression for Small Sample Size Problem",

abstract = "The gradual realization of automation has caused explosive growth of data and increased the amount of researchable data. However, due to the low probability of occurrence and high difficulty in obtaining, representative data is lacking. One of the effective ways to solve this problem is virtual sample generation (VSG). In this study, a novel VSG method is put forward. The sample squares are divided in the input space according to Dominance Analysis, and the virtual inputs are generated by using the Quadrat Density Method in reverse. The corresponding virtual output is predicted by Gaussian Process Regression. Through Quantile Regression, analyze the correlation between input variables and output variables. The generated virtual samples are screened, and the virtual samples that do not meet the correlation relationship are eliminated. In order to verify the effectiveness of the proposed method, experiments are carried out on two numerical simulations and a real-world application from a cascade reaction process for high-density polyethylene. The results show that the method proposed in this paper is superior to other methods.",

keywords = "dominance analysis, quadrat density method, quantile regression, Small sample size problems, virtual sample generation",

author = "Zhu, {Qun Xiong} and Meiyu Zhu and Yuan Xu and He, {Yan Lin}",

note = "Publisher Copyright: {\textcopyright} 2021 IEEE.; 10th IEEE Data Driven Control and Learning Systems Conference, DDCLS 2021 ; Conference date: 14-05-2021 Through 16-05-2021",

year = "2021",

month = may,

day = "14",

doi = "10.1109/DDCLS52934.2021.9455489",

language = "English",

series = "Proceedings of 2021 IEEE 10th Data Driven Control and Learning Systems Conference, DDCLS 2021",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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Zhu, QX, Zhu, M, Xu, Y & He, YL 2021, An Improved Virtual Sample Generation Method Based on Quadrat Density Method and Quantile Regression for Small Sample Size Problem. in M Sun & H Zhang (eds), Proceedings of 2021 IEEE 10th Data Driven Control and Learning Systems Conference, DDCLS 2021., 9455489, Proceedings of 2021 IEEE 10th Data Driven Control and Learning Systems Conference, DDCLS 2021, Institute of Electrical and Electronics Engineers Inc., pp. 854-859, 10th IEEE Data Driven Control and Learning Systems Conference, DDCLS 2021, Suzhou, China, 14/05/21. https://doi.org/10.1109/DDCLS52934.2021.9455489

An Improved Virtual Sample Generation Method Based on Quadrat Density Method and Quantile Regression for Small Sample Size Problem. / Zhu, Qun Xiong; Zhu, Meiyu; Xu, Yuan et al.
Proceedings of 2021 IEEE 10th Data Driven Control and Learning Systems Conference, DDCLS 2021. ed. / Mingxuan Sun; Huaguang Zhang. Institute of Electrical and Electronics Engineers Inc., 2021. p. 854-859 9455489 (Proceedings of 2021 IEEE 10th Data Driven Control and Learning Systems Conference, DDCLS 2021).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - An Improved Virtual Sample Generation Method Based on Quadrat Density Method and Quantile Regression for Small Sample Size Problem

AU - Zhu, Qun Xiong

AU - Zhu, Meiyu

AU - Xu, Yuan

AU - He, Yan Lin

PY - 2021/5/14

Y1 - 2021/5/14

N2 - The gradual realization of automation has caused explosive growth of data and increased the amount of researchable data. However, due to the low probability of occurrence and high difficulty in obtaining, representative data is lacking. One of the effective ways to solve this problem is virtual sample generation (VSG). In this study, a novel VSG method is put forward. The sample squares are divided in the input space according to Dominance Analysis, and the virtual inputs are generated by using the Quadrat Density Method in reverse. The corresponding virtual output is predicted by Gaussian Process Regression. Through Quantile Regression, analyze the correlation between input variables and output variables. The generated virtual samples are screened, and the virtual samples that do not meet the correlation relationship are eliminated. In order to verify the effectiveness of the proposed method, experiments are carried out on two numerical simulations and a real-world application from a cascade reaction process for high-density polyethylene. The results show that the method proposed in this paper is superior to other methods.

AB - The gradual realization of automation has caused explosive growth of data and increased the amount of researchable data. However, due to the low probability of occurrence and high difficulty in obtaining, representative data is lacking. One of the effective ways to solve this problem is virtual sample generation (VSG). In this study, a novel VSG method is put forward. The sample squares are divided in the input space according to Dominance Analysis, and the virtual inputs are generated by using the Quadrat Density Method in reverse. The corresponding virtual output is predicted by Gaussian Process Regression. Through Quantile Regression, analyze the correlation between input variables and output variables. The generated virtual samples are screened, and the virtual samples that do not meet the correlation relationship are eliminated. In order to verify the effectiveness of the proposed method, experiments are carried out on two numerical simulations and a real-world application from a cascade reaction process for high-density polyethylene. The results show that the method proposed in this paper is superior to other methods.

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KW - quadrat density method

KW - quantile regression

KW - Small sample size problems

KW - virtual sample generation

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M3 - Conference contribution

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T3 - Proceedings of 2021 IEEE 10th Data Driven Control and Learning Systems Conference, DDCLS 2021

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BT - Proceedings of 2021 IEEE 10th Data Driven Control and Learning Systems Conference, DDCLS 2021

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A2 - Zhang, Huaguang

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 10th IEEE Data Driven Control and Learning Systems Conference, DDCLS 2021

Y2 - 14 May 2021 through 16 May 2021

ER -

Zhu QX, Zhu M, Xu Y, He YL. An Improved Virtual Sample Generation Method Based on Quadrat Density Method and Quantile Regression for Small Sample Size Problem. In Sun M, Zhang H, editors, Proceedings of 2021 IEEE 10th Data Driven Control and Learning Systems Conference, DDCLS 2021. Institute of Electrical and Electronics Engineers Inc. 2021. p. 854-859. 9455489. (Proceedings of 2021 IEEE 10th Data Driven Control and Learning Systems Conference, DDCLS 2021). doi: 10.1109/DDCLS52934.2021.9455489

An Improved Virtual Sample Generation Method Based on Quadrat Density Method and Quantile Regression for Small Sample Size Problem

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