Shannon information and receiver operating characteristic analysis for multiclass classification in imaging
| Autor: | Johnathan B. Cushing, Eric Clarkson |
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| Rok vydání: | 2016 |
| Předmět: |
Computer Science::Machine Learning
Observer (quantum physics) 01 natural sciences 030218 nuclear medicine & medical imaging 010309 optics Multiclass classification Legendre transformation 03 medical and health sciences symbols.namesake Mathematics::Algebraic Geometry 0302 clinical medicine Optics 0103 physical sciences Mathematics Ideal (set theory) Receiver operating characteristic Mathematics::Complex Variables business.industry Function (mathematics) Integral transform Atomic and Molecular Physics and Optics Electronic Optical and Magnetic Materials Hypersurface symbols Mathematics::Differential Geometry Computer Vision and Pattern Recognition business Algorithm |
| Zdroj: | Journal of the Optical Society of America. A, Optics, image science, and vision. 33(5) |
| ISSN: | 1520-8532 |
| Popis: | We show how Shannon information is mathematically related to receiver operating characteristic (ROC) analysis for multiclass classification problems in imaging. In particular, the minimum probability of error for the ideal observer, as a function of the prior probabilities for each class, determines the Shannon Information for the classification task, also considered as a function of the prior probabilities on the classes. In the process, we show how an ROC hypersurface that has been studied by other researchers is mathematically related to a Shannon information ROC (SIROC) hypersurface. In fact, the ROC hypersurface completely determines the SIROC hypersurface via a non-local integral transform on the ROC hypersurface. We also show that both hypersurfaces are convex and satisfy other geometrical relationships via the Legendre transform. |
| Databáze: | OpenAIRE |
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