Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Velikova, M.: Monotone models for prediction in data mining. PhD thesis, Tilburg University, Tilburg, The Netherlands (2006)
Sill, J.: Monotonic networks. In: Advances in Neural Information Processing Systems (NIPS), vol. 10, pp. 661–667. MIT Press, Cambridge (1998)
Tuy, H.: Monotonic optimization: problems and solution approaches. SIAM Journal on Optimization 11(2), 464–494 (2000)
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)
Armstrong, W.W., Thomas, M.M.: Adaptive logic networks. In: Handbook of Neural Computation, vol. 10, pp. 1–14. Oxford University Press, Oxford (1997)
van Engeland, S., Karssemeijer, N.: Combining two mammographic projections in a computer aided mass detection method. Medical Physics 34(3), 898–905 (2007)
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)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Velikova, M., Daniels, H., Samulski, M. (2008). Partially Monotone Networks Applied to Breast Cancer Detection on Mammograms. In: Kůrková, V., Neruda, R., KoutnÃk, J. (eds) Artificial Neural Networks - ICANN 2008. ICANN 2008. Lecture Notes in Computer Science, vol 5163. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87536-9_94
Download citation
DOI: https://doi.org/10.1007/978-3-540-87536-9_94
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87535-2
Online ISBN: 978-3-540-87536-9
eBook Packages: Computer ScienceComputer Science (R0)