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Convex and Nonconvex Nonparametric Frontier-based Classification Methods for Anomaly Detection

Author

Listed:
  • Qianying JIN

    (College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China)

  • Kristiaan KERSTENS

    (Univ. Lille, CNRS, IESEG School of Management, UMR 9221 - LEM - Lille E´conomie Management, Lille, France)

  • Ignace VAN DE WOESTYNE

    (KU Leuven, Research Centre for Operations Research and Statistics (ORSTAT), Brussels Campus, War- moesberg 26, B-1000 Brussels, Belgium)

Abstract

Effective methods for determining the boundary of the normal class are very useful for detecting anomalies in commercial or security applications - a problem known as anomaly detection. This contribution proposes a nonparametric frontier-based clas- sification (NPFC) method for anomaly detection. By relaxing the commonly used convexity assumption in the literature, a nonconvex NPFC method is constructed and the nonconvex nonparametric frontier turns out to provide a more conservative bound- ary enveloping the normal class. By reflecting on the monotonic relation between the characteristic variables and the membership, the proposed NPFC method is in a more general form since both input-type and output-type characteristic variables are incor- porated. A biomedical data set is used to test the performance of the proposed NPFC methods. The results show that the proposed NPFC methods have competitive clas- sification performance and have consistent advantages in detecting abnormal samples, especially the nonconvex NPFC method

Suggested Citation

  • Qianying JIN & Kristiaan KERSTENS & Ignace VAN DE WOESTYNE, 2023. "Convex and Nonconvex Nonparametric Frontier-based Classification Methods for Anomaly Detection," Working Papers 2023-EQM-01, IESEG School of Management.
    • Handle: RePEc:ies:wpaper:e202302
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    References listed on IDEAS

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    1. Kerstens, Kristiaan & Sadeghi, Jafar & Toloo, Mehdi & Van de Woestyne, Ignace, 2022. "Procedures for ranking technical and cost efficient units: With a focus on nonconvexity," European Journal of Operational Research, Elsevier, vol. 300(1), pages 269-281.
    2. Per Andersen & Niels Christian Petersen, 1993. "A Procedure for Ranking Efficient Units in Data Envelopment Analysis," Management Science, INFORMS, vol. 39(10), pages 1261-1264, October.
    3. Walter Briec & Kristiaan Kerstens & Ignace Van de Woestyne, 2018. "Hypercongestion in production correspondences: an empirical exploration," Applied Economics, Taylor & Francis Journals, vol. 50(27), pages 2938-2956, June.
    4. Lovell, C. A. Knox & Pastor, Jesus T., 1999. "Radial DEA models without inputs or without outputs," European Journal of Operational Research, Elsevier, vol. 118(1), pages 46-51, October.
    5. K Kerstens & I Van de Woestyne, 2011. "Negative data in DEA: a simple proportional distance function approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1413-1419, July.
    6. Bruce G. Marcot & Anca M. Hanea, 2021. "What is an optimal value of k in k-fold cross-validation in discrete Bayesian network analysis?," Computational Statistics, Springer, vol. 36(3), pages 2009-2031, September.
    7. Valero-Carreras, Daniel & Aparicio, Juan & Guerrero, Nadia M., 2021. "Support vector frontiers: A new approach for estimating production functions through support vector machines," Omega, Elsevier, vol. 104(C).
    8. W. Briec, 1997. "A Graph-Type Extension of Farrell Technical Efficiency Measure," Journal of Productivity Analysis, Springer, vol. 8(1), pages 95-110, March.
    9. Sueyoshi, Toshiyuki, 2006. "DEA-Discriminant Analysis: Methodological comparison among eight discriminant analysis approaches," European Journal of Operational Research, Elsevier, vol. 169(1), pages 247-272, February.
    10. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
    11. Juan Aparicio & Miriam Esteve & Jesus J. Rodriguez-Sala & Jose L. Zofio, 2021. "The Estimation of Productive Efficiency Through Machine Learning Techniques: Efficiency Analysis Trees," International Series in Operations Research & Management Science, in: Joe Zhu & Vincent Charles (ed.), Data-Enabled Analytics, pages 51-92, Springer.
    12. Chiwoo Park & Jianhua Z. Huang & Yu Ding, 2010. "A Computable Plug-In Estimator of Minimum Volume Sets for Novelty Detection," Operations Research, INFORMS, vol. 58(5), pages 1469-1480, October.
    13. Esteve, Miriam & Aparicio, Juan & Rodriguez-Sala, Jesus J. & Zhu, Joe, 2023. "Random Forests and the measurement of super-efficiency in the context of Free Disposal Hull," European Journal of Operational Research, Elsevier, vol. 304(2), pages 729-744.
    14. Pendharkar, Parag C., 2002. "A potential use of data envelopment analysis for the inverse classification problem," Omega, Elsevier, vol. 30(3), pages 243-248, June.
    15. Laurens Cherchye & Timo Kuosmanen & Thierry Post, 2001. "FDH Directional Distance Functions with an Application to European Commercial Banks," Journal of Productivity Analysis, Springer, vol. 15(3), pages 201-215, January.
    16. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    17. C F Leon & F Palacios, 2009. "Evaluation of rejected cases in an acceptance system with data envelopment analysis and goal programming," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(10), pages 1411-1420, October.
    18. Kaffash, Sepideh & Azizi, Roza & Huang, Ying & Zhu, Joe, 2020. "A survey of data envelopment analysis applications in the insurance industry 1993–2018," European Journal of Operational Research, Elsevier, vol. 284(3), pages 801-813.
    19. Kim, Ji-Hyun, 2009. "Estimating classification error rate: Repeated cross-validation, repeated hold-out and bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3735-3745, September.
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    Keywords

    : Nonparametric Frontier; Convex; Nonconvex; Anomaly Detection;
    All these keywords.

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