Maximizing upgrading and downgrading margins for ordinal regression

In ordinal regression, a score function and threshold values are sought to classify a set of objects into a set of ranked classes. Classifying an individual in a class with higher (respectively lower) rank than its actual rank is called an upgrading (respectively downgrading) error. Since upgrading and downgrading errors may not have the same importance, they should be considered as two different criteria to be taken into account when measuring the quality of a classifier. In Support Vector Machines, margin maximization is used as an effective and computationally tractable surrogate of the minimization of misclassification errors. As an extension, we consider in this paper the maximization of upgrading and downgrading margins as a surrogate of the minimization of upgrading and downgrading errors, and we address the biobjective problem of finding a classifier maximizing simultaneously the two margins. The whole set of Pareto-optimal solutions of such biobjective problem is described as translations of the optimal solutions of a scalar optimization problem. For the most popular case in which the Euclidean norm is considered, the scalar problem has a unique solution, yielding that all the Pareto-optimal solutions of the biobjective problem are translations of each other. Hence, the Pareto-optimal solutions can easily be provided to the analyst, who, after inspection of the misclassification errors caused, should choose in a later stage the most convenient classifier. The consequence of this analysis is that it provides a theoretical foundation for a popular strategy among practitioners, based on the so-called ROC curve, which is shown here to equal the set of Pareto-optimal solutions of maximizing simultaneously the downgrading and upgrading margins

A phantom-based JAFROC observer study of two CT reconstruction methods : the search for optimisation of lesion detection and effective dose

Purpose: To investigate the dose saving potential of iterative reconstruction (IR) in a computed tomography (CT) examination of the thorax. Materials and Methods: An anthropomorphic chest phantom containing various configurations of simulated lesions (5, 8, 10 and 12mm; +100, -630 and -800 Hounsfield Units, HU) was imaged on a modern CT system over a tube current range (20, 40, 60 and 80mA). Images were reconstructed with (IR) and filtered back projection (FBP). An ATOM 701D (CIRS, Norfolk, VA) dosimetry phantom was used to measure organ dose. Effective dose was calculated. Eleven observers (15.11±8.75 years of experience) completed a free response study, localizing lesions in 544 single CT image slices. A modified jackknife alternative free-response receiver operating characteristic (JAFROC) analysis was completed to look for a significant effect of two factors: reconstruction method and tube current. Alpha was set at 0.05 to control the Type I error in this study. Results: For modified JAFROC analysis of reconstruction method there was no statistically significant difference in lesion detection performance between FBP and IR when figures-of-merit were averaged over tube current (F(1,10)=0.08, p = 0.789). For tube current analysis, significant differences were revealed between multiple pairs of tube current settings (F(3,10) = 16.96, p<0.001) when averaged over image reconstruction method. Conclusion: The free-response study suggests that lesion detection can be optimized at 40mA in this phantom model, a measured effective dose of 0.97mSv. In high-contrast regions the diagnostic value of IR, compared to FBP, is less clear