Binary ROC curve and three-class 2-D ROC surface

Xin He; Eric C. Frey

doi:10.1117/12.844593

Binary ROC curve and three-class 2-D ROC surface

Xin He, Eric C. Frey

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Scopus citations

Abstract

In this work, we compared the binary ROC curve and the 2-D three-class ROC surface. We found that the 2-D three-class ROC surface shares most of the properties of the binary ROC curve. In particular, the curve (or surface) has the same DOF as the as the decision rule that is used to generate it; the curve (or surface) contains all the optimal operating points under various decision criteria (note that for three-class, the equal error utility assumption is assumed, same below); different decision criteria result in the same ROC curve (or surface) by considering all the possible prior information; ROC curve (or surface) uniquely corresponds to one pair (or triplet) of likelihood ratio distributions, assuming such a pair (or triplet) exists; the ROC curve (or surface) is concave; and the ROC curve (or surface) provides graphic information as well as figure-of-merit for task performance. We thus conclude that that the 2-D ROC surface may be preferable as a starting point for comparing systems used to perform 3-class diagnostic tasks.

Original language	English (US)
Title of host publication	Medical Imaging 2010
Subtitle of host publication	Image Perception, Observer Performance, and Technology Assessment
DOIs	https://doi.org/10.1117/12.844593
State	Published - 2010
Externally published	Yes
Event	Medical Imaging 2010: Image Perception, Observer Performance, and Technology Assessment - San Diego, CA, United States Duration: Feb 17 2010 → Feb 18 2010

Publication series

Name	Progress in Biomedical Optics and Imaging - Proceedings of SPIE
Volume	7627
ISSN (Print)	1605-7422

Other

Other	Medical Imaging 2010: Image Perception, Observer Performance, and Technology Assessment
Country/Territory	United States
City	San Diego, CA
Period	2/17/10 → 2/18/10

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Biomaterials
Atomic and Molecular Physics, and Optics
Radiology Nuclear Medicine and imaging

Access to Document

10.1117/12.844593

Cite this

He, X & Frey, EC 2010, Binary ROC curve and three-class 2-D ROC surface. in Medical Imaging 2010: Image Perception, Observer Performance, and Technology Assessment., 762710, Progress in Biomedical Optics and Imaging - Proceedings of SPIE, vol. 7627, Medical Imaging 2010: Image Perception, Observer Performance, and Technology Assessment, San Diego, CA, United States, 2/17/10. https://doi.org/10.1117/12.844593

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abstract = "In this work, we compared the binary ROC curve and the 2-D three-class ROC surface. We found that the 2-D three-class ROC surface shares most of the properties of the binary ROC curve. In particular, the curve (or surface) has the same DOF as the as the decision rule that is used to generate it; the curve (or surface) contains all the optimal operating points under various decision criteria (note that for three-class, the equal error utility assumption is assumed, same below); different decision criteria result in the same ROC curve (or surface) by considering all the possible prior information; ROC curve (or surface) uniquely corresponds to one pair (or triplet) of likelihood ratio distributions, assuming such a pair (or triplet) exists; the ROC curve (or surface) is concave; and the ROC curve (or surface) provides graphic information as well as figure-of-merit for task performance. We thus conclude that that the 2-D ROC surface may be preferable as a starting point for comparing systems used to perform 3-class diagnostic tasks.",

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N2 - In this work, we compared the binary ROC curve and the 2-D three-class ROC surface. We found that the 2-D three-class ROC surface shares most of the properties of the binary ROC curve. In particular, the curve (or surface) has the same DOF as the as the decision rule that is used to generate it; the curve (or surface) contains all the optimal operating points under various decision criteria (note that for three-class, the equal error utility assumption is assumed, same below); different decision criteria result in the same ROC curve (or surface) by considering all the possible prior information; ROC curve (or surface) uniquely corresponds to one pair (or triplet) of likelihood ratio distributions, assuming such a pair (or triplet) exists; the ROC curve (or surface) is concave; and the ROC curve (or surface) provides graphic information as well as figure-of-merit for task performance. We thus conclude that that the 2-D ROC surface may be preferable as a starting point for comparing systems used to perform 3-class diagnostic tasks.

AB - In this work, we compared the binary ROC curve and the 2-D three-class ROC surface. We found that the 2-D three-class ROC surface shares most of the properties of the binary ROC curve. In particular, the curve (or surface) has the same DOF as the as the decision rule that is used to generate it; the curve (or surface) contains all the optimal operating points under various decision criteria (note that for three-class, the equal error utility assumption is assumed, same below); different decision criteria result in the same ROC curve (or surface) by considering all the possible prior information; ROC curve (or surface) uniquely corresponds to one pair (or triplet) of likelihood ratio distributions, assuming such a pair (or triplet) exists; the ROC curve (or surface) is concave; and the ROC curve (or surface) provides graphic information as well as figure-of-merit for task performance. We thus conclude that that the 2-D ROC surface may be preferable as a starting point for comparing systems used to perform 3-class diagnostic tasks.

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Binary ROC curve and three-class 2-D ROC surface

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