IDEAS home Printed from https://ideas.repec.org/p/ies/wpaper/e202302.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: https://www.ieseg.fr/wp-content/uploads/2023/02/2023-EQM-01.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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).
    4. W. Briec, 1997. "A Graph-Type Extension of Farrell Technical Efficiency Measure," Journal of Productivity Analysis, Springer, vol. 8(1), pages 95-110, March.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ravelojaona, Paola, 2019. "On constant elasticity of substitution – Constant elasticity of transformation Directional Distance Functions," European Journal of Operational Research, Elsevier, vol. 272(2), pages 780-791.
    2. Aparicio, Juan & Pastor, Jesus T. & Vidal, Fernando, 2016. "The directional distance function and the translation invariance property," Omega, Elsevier, vol. 58(C), pages 1-3.
    3. Mahmood Mehdiloo & Jafar Sadeghi & Kristiaan Kerstens, 2024. "Top Down Axiomatic Modeling of Metatechnologies and Evaluating Directional Economic Efficiency," Working Papers 2024-EQM-03, IESEG School of Management.
    4. Halická, Margaréta & Trnovská, Mária & Černý, Aleš, 2024. "A unified approach to radial, hyperbolic, and directional efficiency measurement in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 312(1), pages 298-314.
    5. Kristiaan Kerstens & Ignace Van de Woestyne, 2018. "Enumeration algorithms for FDH directional distance functions under different returns to scale assumptions," Annals of Operations Research, Springer, vol. 271(2), pages 1067-1078, December.
    6. Bogetoft, Peter & Leth Hougaard, Jens, 2004. "Super efficiency evaluations based on potential slack," European Journal of Operational Research, Elsevier, vol. 152(1), pages 14-21, January.
    7. Cherchye, L. & Post, G.T., 2001. "Methodological Advances in Dea," ERIM Report Series Research in Management ERS-2001-53-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    8. J.Ph. Boussemart & K. Kerstens & S. Blancard & W. Briec, 2007. "Technology Adoption in French Agriculture and the role of Financial Constraints," Post-Print hal-00287974, HAL.
    9. Jean-Philippe Boussemart & Walter Briec & Christophe Tavera, 2011. "More evidence on technological catching-up in the manufacturing sector," Applied Economics, Taylor & Francis Journals, vol. 43(18), pages 2321-2330.
    10. H Leleu, 2009. "Mixing DEA and FDH models together," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(12), pages 1730-1737, December.
    11. Macedo, Pedro & Scotto, Manuel, 2014. "Cross-entropy estimation in technical efficiency analysis," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 124-130.
    12. Pastor, Jesus T. & Lovell, C.A. Knox & Aparicio, Juan, 2020. "Defining a new graph inefficiency measure for the proportional directional distance function and introducing a new Malmquist productivity index," European Journal of Operational Research, Elsevier, vol. 281(1), pages 222-230.
    13. W. Briec & K. Kerstens, 2009. "Infeasibility and Directional Distance Functions with Application to the Determinateness of the Luenberger Productivity Indicator," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 55-73, April.
    14. Jean‐Philippe Boussemart & Walter Briec & Kristiaan Kerstens & Jean‐Christophe Poutineau, 2003. "Luenberger and Malmquist Productivity Indices: Theoretical Comparisons and Empirical Illustration," Bulletin of Economic Research, Wiley Blackwell, vol. 55(4), pages 391-405, October.
    15. Silva, Elvira & Lansink, Alfons Oude & Stefanou, Spiro E., 2015. "The adjustment-cost model of the firm: Duality and productive efficiency," International Journal of Production Economics, Elsevier, vol. 168(C), pages 245-256.
    16. Blancard, Stephane & Boussemart, Jean-Philippe & Crainich, D. & Leleu, Herve, 2008. "How can allocative inefficiency reveal risk preference? An empirical investigation on French wheat farms," 2008 International Congress, August 26-29, 2008, Ghent, Belgium 44208, European Association of Agricultural Economists.
    17. Maria Silva Portela & Pedro Borges & Emmanuel Thanassoulis, 2003. "Finding Closest Targets in Non-Oriented DEA Models: The Case of Convex and Non-Convex Technologies," Journal of Productivity Analysis, Springer, vol. 19(2), pages 251-269, April.
    18. Papaioannou, Grammatoula & Podinovski, Victor V., 2023. "Multicomponent production technologies with restricted allocations of shared inputs and outputs," European Journal of Operational Research, Elsevier, vol. 308(1), pages 274-289.
    19. Kao, Chiang, 2020. "Measuring efficiency in a general production possibility set allowing for negative data," European Journal of Operational Research, Elsevier, vol. 282(3), pages 980-988.
    20. Mercedes Beltrán-Esteve & José Gómez-Limón & Andrés Picazo-Tadeo & Ernest Reig-Martínez, 2014. "A metafrontier directional distance function approach to assessing eco-efficiency," Journal of Productivity Analysis, Springer, vol. 41(1), pages 69-83, February.

    More about this item

    Keywords

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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ies:wpaper:e202302. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Lies BOUTEN (email available below). General contact details of provider: https://edirc.repec.org/data/iesegfr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.