Optimization of an ROC hypersurface constructed only from an observer's within-class sensitivities

Darrin C. Edwards; Charles E. Metz

doi:10.1117/12.654026

17 March 2006 Optimization of an ROC hypersurface constructed only from an observer's within-class sensitivities

Darrin C. Edwards, Charles E. Metz

Proceedings Volume 6146, Medical Imaging 2006: Image Perception, Observer Performance, and Technology Assessment; 61460A (2006) https://doi.org/10.1117/12.654026
Event: Medical Imaging, 2006, San Diego, California, United States

Abstract

We have shown in previous work that an ideal observer in a classification task with N classes achieves the optimal receiver operating characteristic (ROC) hypersurface in a Neyman-Pearson sense. That is, the hypersurface obtained by taking one of the ideal observer's misclassification probabilities as a function of the other N²-N-1 misclassification probabilities is never above the corresponding hypersurface obtained by any other observer. Due to the inherent complexity of evaluating observer performance in an N-class classification task with N>2, some researchers have suggested a generally incomplete but more tractable evaluation in terms of a hypersurface plotting only the N "sensitivities" (the probabilities of correctly classifying observations in the various classes). An N-class observer generally has up to N²-N-1 degrees of freedom, so a given sensitivity will still vary when the other N-1 are held fixed; a well-defined hypersurface can be constructed by considering only the maximum possible value of one sensitivity for each achievable value of the other N-1. We show that optimal performance in terms of this generally incomplete performance descriptor, in a Neyman-Pearson sense, is still achieved by the N-class ideal observer. That is, the hypersurface obtained by taking the maximal value of one of the ideal observer's correct classification probabilities as a function of the other N-1 is never below the corresponding hypersurface obtained by any other observer.

Citation Download Citation

Darrin C. Edwards and Charles E. Metz "Optimization of an ROC hypersurface constructed only from an observer's within-class sensitivities", Proc. SPIE 6146, Medical Imaging 2006: Image Perception, Observer Performance, and Technology Assessment, 61460A (17 March 2006); https://doi.org/10.1117/12.654026

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