Advertisement

A multi-level knee point based multi-objective evolutionary algorithm for AUC maximization

  • Jianfeng Qiu
  • Minghui Liu
  • Lei Zhang
  • Wei Li
  • Fan ChengEmail author
Regular Research Paper
  • 2 Downloads

Abstract

The area under receiver operating characteristic curve (AUC) is one of the widely used metrics for measuring imbalanced data classification results. Designing multi-objective evolutionary algorithms for AUC maximization problem has attracted much attention of researchers recently. However, most of these methods either search the Pareto front directly, or perform tailored convex hull search for AUC maximization. None of them take the advantage of multi-level knee points found in the process of evolution for AUC maximization. To this end, this paper proposes a multi-level knee point based multi-objective evolutionary algorithm (named MKnEA-AUC) for AUC maximization on the basis of a recently developed knee point driven evolutionary algorithm for multi/many-objective optimization. In MKnEA-AUC, an adaptive clustering strategy is proposed for automatically determining the knee points on the current population. By utilizing the preference of found knee points, the evolution of the population can converge quickly. We verify the effectiveness of the proposed algorithm MKnEA-AUC on 13 widely used benchmark data sets and the experimental results demonstrate that MKnEA-AUC is superior over the state-of-the-art algorithms for AUC maximization.

Keywords

AUC maximization Multi-objective evolutionary algorithm Knee points Adaptive clustering strategy 

Notes

Acknowledgements

This work is supported by National Nature Science Foundation of China (Grant Nos. 61502001, 61502004), Scientific Research Startup Fund for Doctors of Anhui University, by the Academic and Technology Leader Imported Project of Anhui University (No. J01006057). This work was also supported in part by the Natural Science Foundation of Anhui Province (Grant No. 1708085MF166), Humanities and Social Sciences Project of Chinese Ministry of Education (Grant No. 18YJC870004) and Key Program of Natural Science Project of Educational Commission of Anhui Province (Grant No. KJ2017A013).

References

  1. 1.
    Yang Z, Zhang T, Lu J, Zhang D, Kalui D (2017) Optimizing area under the ROC curve via extreme learning machines. Knowl Based Syst 130(15):74–89CrossRefGoogle Scholar
  2. 2.
    Welleck SJ (2016) Efficient AUC optimization for information ranking applications. In: European conference on information retrieval, pp 159–170Google Scholar
  3. 3.
    Goin JE (1982) ROC curve estimation and hypothesis testing: applications to breast cancer detection. Pattern Recognit 15(3):263–269CrossRefzbMATHGoogle Scholar
  4. 4.
    Matey JR, Quinn GW, Grother P, Tabassi E, Watson C, Wayman JL (2015) Modest proposals for improving biometric recognition papers. In: IEEE International conference on biometrics theory, applications and systems, pp 1–7Google Scholar
  5. 5.
    Hong W, Tang K (2016) Convex hull-based multi-objective evolutionary computation for maximizing receiver operating characteristics performance. Memet Comput 8:35–44CrossRefGoogle Scholar
  6. 6.
    Cheng R, Jin Y, Narukawa K, Sendhoff B (2015) A multiobjective evolutionary algorithm using Gaussian process-based inverse modeling. IEEE Trans Evolut Comput 19(6):838–856CrossRefGoogle Scholar
  7. 7.
    Zhang X, Tian Y, Cheng R, Jin Y (2018) A decision variable clustering-based evolutionary algorithm for large-scale many-objective optimization. IEEE Trans Evolut Comput 22(1):97–112CrossRefGoogle Scholar
  8. 8.
    Sun C, Ding J, Zeng J, Jin Y (2016) A fitness approximation assisted competitive swarm optimizer for large scale expensive optimization problems. Memet Comput 10(2):123–134CrossRefGoogle Scholar
  9. 9.
    Tian Y, Cheng R, Zhang X, Cheng F, Jin Y (2018) An indicator based multi-objective evolutionary algorithm with reference point adaptation for better versatility. IEEE Trans Evolut Comput 22(4):609–622CrossRefGoogle Scholar
  10. 10.
    Kupinski MA, Anastasio MA (1999) Multiobjective genetic optimization of diagnostic classifiers with implications for generating receiver operating characteristic curves. IEEE Trans Med Imaging 18(8):675–685CrossRefGoogle Scholar
  11. 11.
    Gräning L, Jin Y, Sendhoff B (2006) Generalization improvement in multi-objective learning. In: International joint conference on neural networks, pp 4839–4846Google Scholar
  12. 12.
    Provost F, Fawcett T (2001) Robust classification for imprecise environments. Mach Learn 42(3):203–231CrossRefzbMATHGoogle Scholar
  13. 13.
    Wang P, Tang K, Weise T, Tsang E, Yao X (2014) Multiobjective genetic programming for maximizing ROC performance. Neurocomputing 125(3):102–118CrossRefGoogle Scholar
  14. 14.
    Wang P, Emmerich M, Li R, Tang K, Bäck T, Yao X (2015) Convex hull-based multiobjective genetic programming for maximizing receiver operating characteristic performance. IEEE Trans Evolut Comput 19(2):188–200CrossRefGoogle Scholar
  15. 15.
    Cococcioni M, Ducange P, Lazzerini B, Marcelloni F (2007) A new multi-objective evolutionary algorithm based on convex hull for binary classifier optimization. In: IEEE congress on evolutionary computation, pp 3150–3156Google Scholar
  16. 16.
    Wang P, Emmerich M, Li R, Tang K, Baeck T, Yao X (2013) Convex hull-based multi-objective genetic programming for maximizing ROC performance. Neurocomputing 125(3):102–118Google Scholar
  17. 17.
    Ducange P, Lazzerini B, Marcelloni F (2010) Multi-objective genetic fuzzy classifiers for imbalanced and cost-sensitive datasets. Soft Comput 14(7):713–728CrossRefGoogle Scholar
  18. 18.
    Zhang X, Tian Y, Jin Y (2015) A knee point-driven evolutionary algorithm for many-objective optimization. IEEE Trans Evolut Comput 19(6):761–776CrossRefGoogle Scholar
  19. 19.
    Bhowan U, Johnston M, Zhang M, Yao X (2013) Evolving diverse ensembles using genetic programming for classification with unbalanced data. IEEE Trans Evolut Comput 17(3):368–386CrossRefGoogle Scholar
  20. 20.
    Chatelain C, Adam S, Lecourtier Y, Heutte L, Paquet T (2010) A multi-model selection framework for unknown and/or evolutive misclassification cost problems. Pattern Recognit 43(3):815–823CrossRefzbMATHGoogle Scholar
  21. 21.
    While L, Hingston P, Barone L, Huband S (2006) A faster algorithm for calculating hypervolume. IEEE Trans Evolut Comput 10(1):29–38CrossRefGoogle Scholar
  22. 22.
    Li M, Zheng J (2009) Spread assessment for evolutionary multi-objective optimization. In: International conference on evolutionary multi-criterion optimization, pp 216–230Google Scholar
  23. 23.
    Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evolut Comput 6(2):182–197CrossRefGoogle Scholar
  24. 24.
    Zhang Q, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evolut Comput 11(6):712–731CrossRefGoogle Scholar
  25. 25.
    Joachims T (2005) A support vector method for multivariate performance measures. In: Proceedings of the 22nd international conference on machine learning, pp 377–384Google Scholar
  26. 26.
    Deb K, Agrawal RB (1995) Simulated binary crossover for continuous search space. Complex Syst 9(4):115–148MathSciNetzbMATHGoogle Scholar
  27. 27.
    Deb K, Goyal M (1996) A combined genetic adaptive search (geneas) for engineering design. Comput Sci Inform 26(4):30–45Google Scholar
  28. 28.
    Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, New YorkzbMATHGoogle Scholar
  29. 29.
    Zhang X, Tian Y, Cheng R, Jin Y (2015) An efficient approach to nondominated sorting for evolutionary multiobjective optimization. IEEE Trans Evolut Comput 19(2):201–213CrossRefGoogle Scholar
  30. 30.
    Tian Y, Cheng R, Zhang X, Jin Y (2017) PlatEMO: a matlab platform for evolutionary multi-objective optimization. IEEE Comput Intell Mag 12(4):73–87CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Jianfeng Qiu
    • 1
    • 2
  • Minghui Liu
    • 2
  • Lei Zhang
    • 1
    • 2
  • Wei Li
    • 1
    • 2
  • Fan Cheng
    • 1
    • 2
    Email author
  1. 1.Key Lab of Intelligent Computing and Signal Processing of Ministry of EducationAnhui UniversityHefeiChina
  2. 2.School of Computer Science and TechnologyAnhui UniversityHefeiChina

Personalised recommendations