Abstract
A well established technique to improve the classification performances is to combine more classifiers. In the binary case, an effective instrument to analyze the dichotomizers under different class and cost distributions providing a description of their performances at different operating points is the Receiver Operating Characteristic (ROC) curve. To generate a ROC curve, the outputs of the dichotomizers have to be processed. An alternative way that makes this analysis more tractable with mathematical tools is to use a parametric model and, in particular, the binormal model that gives a good approximation to many empirical ROC curves. Starting from this model, we propose a method to estimate the ROC curve of the linear combination of two dichotomizers given the ROC curves of the single classifiers. A possible application of this approach has been successfully tested on real data set.
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Keywords
- Support Vector Machine
- True Positive Rate
- Multi Layer Perceptron
- Cumulative Distribution Function
- Pima Indian Diabetes
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References
Provost, F., Fawcett, T., Kohavi, R.: The case against accuracy estimation for comparing induction algorithms. In: Proc. 15th Intl. Conf. on Machine Learning, pp. 445–453. Morgan Kaufmann, San Francisco (1998)
Egan, J.P.: Signal detection theory and ROC analysis. Series in Cognition and Perception. Academic Press, New York (1975)
Metz, C.E.: ROC methodology in radiologic imaging. Invest. Radiol. 21, 720–733 (1986)
Bradley, A.P.: The use of the area under the ROC curve in the evaluation of machine learning algorithms. Pattern Recognition 30, 1145–1159 (1997)
Provost, F., Fawcett, T.: Robust classification for imprecise environments. Machine Learning 42, 203–231 (2001)
Tortorella, F.: A ROC-based Reject Rule for Dichotomizers. Pattern Recognition Letters 26, 167–180 (2005)
Fawcett, T.: ROC graphs: notes and practical considerations for data mining researchers. HP Labs Tech Report HPL-2003-4 (2003)
Metz, C.E., Herman, B.A., Shen, J.H.: Maximum-likelihood estimation of ROC curves from continuously-distributed data. Statistics in Medicine 17, 1033–1053 (1998)
Pepe, M.S.: The Statistical Evaluation of Medical Tests for Classification and Prediction. Oxford Statistical Science Series. Oxford University Press, Oxford (2003)
Papoulis, A.: Probability, Random Variables, and Stochastic Processes. McGraw-Hill, New York (2001)
Cortes, C., Mohri, M.: AUC Optimization vs. Error Rate Minimization. Advances in Neural Information Processing Systems. In: NIPS 2003 (2004)
Flake, G.W., Pearlmuter, B.A.: Differentiating Functions of the Jacobian with Respect to the Weights. In: Solla, S.A., Leen, T.K., Müller, K. (eds.) Advances in Neural Information Processing Systems, vol. 12. The MIT Press, Cambridge (2000)
Blake, C., Keogh, E., Merz, C.J.: UCI Repository of Machine Learning Databases (1998), http://www.ics.uci.edu/~mlearn/MLRepository.html
Metz, C.E., Pan, X.: Proper binormal ROC curves: theory and maximum-likelihood estimation. J. Math. Psych. 43, 1–33 (1999)
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© 2005 Springer-Verlag Berlin Heidelberg
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Marrocco, C., Molinara, M., Tortorella, F. (2005). Estimating the ROC Curve of Linearly Combined Dichotomizers. In: Roli, F., Vitulano, S. (eds) Image Analysis and Processing – ICIAP 2005. ICIAP 2005. Lecture Notes in Computer Science, vol 3617. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11553595_95
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DOI: https://doi.org/10.1007/11553595_95
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28869-5
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