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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
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Three-class ROC analysis--toward a general decision theoretic solution.

Xin He1, Brandon D Gallas, Eric C Frey

  • 1Department of Radiology, Johns Hopkins School of Medicine, Baltimore, MD 21287, USA. xinhe@jhmi.edu

IEEE Transactions on Medical Imaging
|November 4, 2009
PubMed
Summary
This summary is machine-generated.

This study simplifies multiclass receiver operating characteristic (ROC) analysis by reducing the complexity of three-class problems. The 2-D ROC surface uniquely describes optimal classifier performance, offering a complete descriptor for likelihood ratio classifiers.

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Area of Science:

  • Machine Learning
  • Statistical Analysis
  • Pattern Recognition

Background:

  • Multiclass receiver operating characteristic (ROC) analysis remains a theoretical challenge since the advent of binary ROC analysis.
  • Previous work established a three-class ROC analysis paradigm unifying decision theoretic, linear discriminant analysis, and probabilistic foundations.
  • The equal error utility (EEU) assumption was crucial for reducing the dimensionality of the three-class ROC analysis space.

Purpose of the Study:

  • To demonstrate that the 2-D ROC surface fully and uniquely describes optimal performance for three-class classification tasks.
  • To establish the equivalence between the 2-D sensitivity-space ROC surface and the triplet of likelihood ratio distributions.
  • To provide a complete descriptor for the optimal performance of likelihood ratio classifiers in three-class settings.

Main Methods:

  • Reduction of the intrinsic 5-D hypersurface of three-class ROC analysis to a 2-D surface in sensitivity space using the EEU assumption.
  • Mathematical proof establishing the conditions under which two classifiers share the same triplet of likelihood ratio distributions.
  • Analysis of classifiers utilizing continuous and differentiable 2-D sensitivity-space ROC surfaces.

Main Results:

  • The 2-D ROC surface in sensitivity space is proven to be a complete and unique descriptor for optimal three-class classification performance.
  • A direct equivalence is shown between having identical 2-D sensitivity-space ROC surfaces and identical triplets of likelihood ratio distributions for classifiers.
  • The 2-D sensitivity surface encapsulates all information regarding optimal three-class task performance for likelihood ratio classifiers.

Conclusions:

  • The 2-D sensitivity-space ROC surface provides a comprehensive characterization of optimal performance for three-class classification tasks.
  • This finding simplifies the theoretical landscape of multiclass ROC analysis, offering a more tractable approach.
  • The established equivalence facilitates the evaluation and comparison of likelihood ratio classifiers in three-class scenarios.