Partially Monotone Networks Applied to Breast Cancer Detection on Mammograms

  • Marina Velikova
  • Hennie Daniels
  • Maurice Samulski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5163)


In many prediction problems it is known that the response variable depends monotonically on most of the explanatory variables but not on all. Often such partially monotone problems cannot be accurately solved by unconstrained methods such as standard neural networks. In this paper we propose so-called MIN-MAX networks that are partially monotone by construction. We prove that this type of networks have the uniform approximation property, which is a generalization of the result by Sill on totally monotone networks. In a case study on breast cancer detection on mammograms we show that enforcing partial monotonicity constraints in MIN-MAX networks leads to models that not only comply with the domain knowledge but also outperform in terms of accuracy standard neural networks especially if the data set is relative small.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Velikova, M.: Monotone models for prediction in data mining. PhD thesis, Tilburg University, Tilburg, The Netherlands (2006)Google Scholar
  2. 2.
    Sill, J.: Monotonic networks. In: Advances in Neural Information Processing Systems (NIPS), vol. 10, pp. 661–667. MIT Press, Cambridge (1998)Google Scholar
  3. 3.
    Tuy, H.: Monotonic optimization: problems and solution approaches. SIAM Journal on Optimization 11(2), 464–494 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Daniels, H., Velikova, M.: Derivation of monotone decision models from noisy data. IEEE Trans. on Systems, Man and Cybernetics, Part C 36(5), 705–710 (2006)CrossRefGoogle Scholar
  5. 5.
    Armstrong, W.W., Thomas, M.M.: Adaptive logic networks. In: Handbook of Neural Computation, vol. 10, pp. 1–14. Oxford University Press, Oxford (1997)Google Scholar
  6. 6.
    van Engeland, S., Karssemeijer, N.: Combining two mammographic projections in a computer aided mass detection method. Medical Physics 34(3), 898–905 (2007)CrossRefGoogle Scholar
  7. 7.
    Hanley, J.A., McNeil, B.J.: The meaning and use of the area under a Receiver Operating Characteristic (ROC) curve. Radiology 143, 29–36 (1982)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Marina Velikova
    • 1
  • Hennie Daniels
    • 2
    • 3
  • Maurice Samulski
    • 1
  1. 1.Department of RadiologyRadboud University Nijmegen Medical CentreNijmegenThe Netherlands
  2. 2.Rotterdam School of ManagementErasmus UniversityRotterdam
  3. 3.Center for Economic ResearchTilburg UniversityTilburgThe Netherlands

Personalised recommendations