Analysis of <i>k</i>-partite ranking algorithm in area under the receiver operating characteristic curve criterion

Gao, Wei; Wang, Weifan

doi:10.1080/00207160.2017.1322688

Cited by 37 publications

(7 citation statements)

References 18 publications

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“…For statistical analysis, the model of the paired t -test with an alpha of 0.05 was adopted using Statistics and Machine Learning Toolbox in MATLAB (R2021b, MathWorks, MA, USA). When we validated the standard normal distribution of the original object data using criteria that corresponded to both the mean and standard deviation (SD), the results for all raw data showed normality [ 42 , 43 , 44 ]. When the null hypothesis is rejected (h = 0), it means that two samples are not significantly different.…”

Section: Methodsmentioning

confidence: 99%

Quantitative Assessment of the Restoration of Original Anatomy after 3D Virtual Reduction of Long Bone Fractures

Kim

Yoon²,

Shin

et al. 2022

Diagnostics

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Background: The purpose of this study was to demonstrate the usefulness of 3D image-based virtual reduction by validating the evaluation criteria according to guidelines suggested by the AO Surgery Reference. Methods: For this experiment, 19 intact radial ORTHObones (ORTHObones radius, 3B Scientific, Germany, Hamburg) without any fractures were prepared. All ORTHObones with six cortical marking holes (three points on the distal part and three points on the proximal part) were scanned using a CT scanner twice (before/after intentional fracture of the ORTHObone). After the virtual reduction of all 19 ORTHObones, accuracy evaluations using the four criteria (length variation, apposition variation, alignment variation, Rotation Variation) suggested in the AO Surgery Reference were performed. Results: The mean (M) length variation was 0.42 mm, with 0.01 mm standard deviation (SD). The M apposition variation was 0.48 mm, with 0.40 mm SD. The M AP angulation variation (for alignment variation) was 3.24°, with 2.95° SD. The M lateral angulation variation (for alignment variation) was 0.09°, with 0.13° SD. The M angle of axial rotation was 1.27° with SD: 1.19°. Conclusions: The method of accuracy evaluation used in this study can be helpful in establishing a reliable plan.

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Section: Methodsmentioning

confidence: 99%

Quantitative Assessment of the Restoration of Original Anatomy after 3D Virtual Reduction of Long Bone Fractures

Kim

Yoon²,

Shin

et al. 2022

Diagnostics

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“…The first direction of studies focuses on the multipartite ranking problem, which is a natural extension of the bipartite ranking problem where the order is presented with more than two discrete degrees. Hitherto, a substantial amount of efforts have been made to explore the AUC optimization method/theory for the multipartite ranking problem [11], [13], [24], [63], [69]. Moreover, a recent work [66] proposes a novel nonlinear semi-supervised multipartite ranking problem for large-scale datasets.…”

Section: Related Workmentioning

confidence: 99%

Learning With Multiclass AUC: Theory and Algorithms

Yang

Bao

et al. 2022

IEEE Trans. Pattern Anal. Mach. Intell.

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The Area under the ROC curve (AUC) is a well-known ranking metric for problems such as imbalanced learning and recommender systems. The vast majority of existing AUC-optimization-based machine learning methods only focus on binary-class cases, while leaving the multiclass cases unconsidered. In this paper, we start an early trial to consider the problem of learning multiclass scoring functions via optimizing multiclass AUC metrics. Our foundation is based on the M metric, which is a wellknown multiclass extension of AUC. We first pay a revisit to this metric, showing that it could eliminate the imbalance issue from the minority class pairs. Motivated by this, we propose an empirical surrogate risk minimization framework to approximately optimize the M metric. Theoretically, we show that: (i) optimizing most of the popular differentiable surrogate losses suffices to reach the Bayes optimal scoring function asymptotically; (ii) the training framework enjoys an imbalance-aware generalization error bound, which pays more attention to the bottleneck samples of minority classes compared with the traditional O( 1/N ) result. Practically, to deal with the low scalability of the computational operations, we propose acceleration methods for three popular surrogate loss functions, including the exponential loss, squared loss, and hinge loss, to speed up loss and gradient evaluations. Finally, experimental results on 11 real-world datasets demonstrate the effectiveness of our proposed framework.

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“…Then, the applied boundary conditions are dened according to the physics of the problem. [42][43][44][45][46][47][48][49][50][51] Since most of the engineering-related problems contain nonlinear terms in the main governing equations, various techniques have been developed to solve these equations.…”

Section: Problem Definitionmentioning

confidence: 99%

A numerical simulation for magnetohydrodynamic nanofluid flow and heat transfer in rotating horizontal annulus with thermal radiation

et al. 2019

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The impact of an axial magnetic field on the heat transfer and nanofluid flow among two horizontal coaxial tubes in the presence of thermal radiation was considered in this study. The impact of viscous dissipation was also considered. The well-known KKL (Koo-Kleinsteuer-Li) model was applied to approximate the viscosity of the nanofluid and the effective thermal conductivity. Furthermore, proper transformations for the velocity and temperature were applied in this study to obtain a set of ODEs (ordinary differential equations) for basic equations governing the flow, heat and mass transfer. In addition, the 4th order Runge-Kutta (RK) numerical scheme was applied to solve the differential equations along with the associated boundary conditions. The impacts of different parameters, including Hartmann number, Reynolds number, radiation parameter and aspect ratio, on the heat transfer and flow features were studied. According to the results, the value of the Nusselt number increases with an increase in the radiation parameter, Hartmann number and aspect ratio and a decrease in the Reynolds number and Eckert number. Fig. 8 Effect of aspect ratio on the Nusselt number and skin friction coefficient when Pr ¼ 6.8, h ¼ 0.5, Ec ¼ 0.01, Rd ¼ 0.1, Re ¼ 1, f ¼ 0.04.

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Analysis of k-partite ranking algorithm in area under the receiver operating characteristic curve criterion

Cited by 37 publications

References 18 publications

Quantitative Assessment of the Restoration of Original Anatomy after 3D Virtual Reduction of Long Bone Fractures

Quantitative Assessment of the Restoration of Original Anatomy after 3D Virtual Reduction of Long Bone Fractures

Learning With Multiclass AUC: Theory and Algorithms

A numerical simulation for magnetohydrodynamic nanofluid flow and heat transfer in rotating horizontal annulus with thermal radiation

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