Ideal observers and optimal ROC hypersurfaces in N-class classification

IEEE Transactions on Medical Imaging
Darrin C EdwardsMatthew A Kupinski

Abstract

The likelihood ratio, or ideal observer, decision rule is known to be optimal for two-class classification tasks in the sense that it maximizes expected utility (or, equivalently, minimizes the Bayes risk). Furthermore, using this decision rule yields a receiver operating characteristic (ROC) curve which is never above the ROC curve produced using any other decision rule, provided the observer's misclassification rate with respect to one of the two classes is chosen as the dependent variable for the curve (i.e., an "inversion" of the more common formulation in which the observer's true-positive fraction is plotted against its false-positive fraction). It is also known that for a decision task requiring classification of observations into N classes, optimal performance in the expected utility sense is obtained using a set of N-1 likelihood ratios as decision variables. In the N-class extension of ROC analysis, the ideal observer performance is describable in terms of an (N2-N-1)-parameter hypersurface in an (N2-N)-dimensional probability space. We show that the result for two classes holds in this case as well, namely that the ROC hypersurface obtained using the ideal observer decision rule is never above the ROC hypersurface ob...Continue Reading

References

Oct 1, 1978·Seminars in Nuclear Medicine·C E Metz
Jan 23, 1999·Medical Decision Making : an International Journal of the Society for Medical Decision Making·D Mossman
Aug 10, 2000·Medical Decision Making : an International Journal of the Society for Medical Decision Making·S DreiseitlM Binder

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Citations

Jan 1, 2008·Radiological Physics and Technology·Charles E Metz
Aug 10, 2013·Medical Physics·Nicholas PetrickHeang-Ping Chan
Nov 20, 2012·Journal of Mathematical Psychology·Darrin C Edwards, Charles E Metz
Mar 29, 2008·IEEE Transactions on Pattern Analysis and Machine Intelligence·Thomas C W Landgrebe, Robert P W Duin
Nov 4, 2009·IEEE Transactions on Medical Imaging·Xin HeEric C Frey
May 3, 2008·IEEE Transactions on Medical Imaging·Xin He, Eric C Frey
Oct 24, 2007·IEEE Transactions on Medical Imaging·Darrin C Edwards, Charles E Metz
Jan 25, 2007·IEEE Transactions on Medical Imaging·Xin He, Eric C Frey
Jan 28, 2009·IEEE Transactions on Information Technology in Biomedicine : a Publication of the IEEE Engineering in Medicine and Biology Society·Mehul P SampatMia K Markey
Dec 16, 2005·IEEE Transactions on Medical Imaging·Parmeshwar Khurd, Gene Gindi
Mar 10, 2005·IEEE Transactions on Medical Imaging·Darrin C EdwardsRobert M Nishikawa
Apr 4, 2008·Medical Physics·Elizabeth A Krupinski, Yulei Jiang
Jan 15, 2013·EURASIP Journal on Bioinformatics & Systems Biology·Wenlong TangYu-Ping Wang
Mar 8, 2018·Physics in Medicine and Biology·Nancy A Obuchowski, Jennifer A Bullen
Dec 15, 2005·IEEE Transactions on Medical Imaging·Darrin C Edwards, Charles E Metz
May 4, 2016·Journal of the Optical Society of America. A, Optics, Image Science, and Vision·Eric Clarkson, Johnathan B Cushing

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