期刊
IEEE TRANSACTIONS ON MEDICAL IMAGING
卷 23, 期 7, 页码 891-895出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TMI.2004.828358
关键词
ROC analysis; ideal observer; N-class classification
类别
资金
- NCI NIH HHS [R01-CA60187] Funding Source: Medline
- NIBIB NIH HHS [R01 EB002146-02, R01 EB002146, R01 EB002146-03, R01 EB002146-01A1] Funding Source: Medline
- NIGMS NIH HHS [R01-GM57622] Funding Source: Medline
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 - I likelihood ratios as decision variables. In the N-class extension of ROC analysis, the ideal observer performance is describable in terms of an (N-2 - N - 1) -parameter hypersurface in an (N-2 - 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 obtained using any other decision rule (where in our formulation performance is given exclusively with respect to between-class error rates rather than within-class sensitivities).
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