Optimization of restricted ROC surfaces in three-class classification tasks

Area of Science:

• Medical Imaging
• Statistical Decision Theory
• Machine Learning

Background:

• Evaluating observer performance in multi-class classification tasks is complex.
• Simplified Receiver Operating Characteristic (ROC) surfaces are often used for tractability.
• The N-class ideal observer optimizes ROC hypersurface in a Neyman-Pearson sense.

Purpose of the Study:

• To analyze and compare different formulations for evaluating observer performance.
• To determine if simplified ROC surface evaluations are equivalent to maximizing expected utility.
• To investigate the mathematical equivalence of Neyman-Pearson optimization and expected utility maximization.

Main Methods:

• Applied the Neyman-Pearson criterion to four formulations of observer performance evaluation.
• Analyzed simplified ROC surfaces, including the
• Main_Results

Main Results:

• Optimization using the Neyman-Pearson criterion and maximization of expected utility yield equivalent results for restricted cases.
• The analyzed ROC surface formulations provide a complete description of observer performance in an expected utility sense.
• Mathematical equivalence was demonstrated between the two optimization methods.

Conclusions:

• Simplified ROC surface evaluations are mathematically equivalent to expected utility maximization.
• The Neyman-Pearson framework provides a robust method for assessing observer performance across various formulations.
• This research simplifies the evaluation of diagnostic accuracy in complex classification scenarios.