HandTill2001 swMATH ID: 11200 Software Authors: Hand, David J.; Till, Robert J.; Andreas Dominik Cullmann; Edgar Kublin Description: A simple generalisation of the area under the ROC curve for multiple class classification problems The area under the ROC curve, or the equivalent Gini index, is a widely used measure of performance of supervised classification rules. It has the attractive property that it side-steps the need to specify the costs of the different kinds of misclassification. However, the simple form is only applicable to the case of two classes. We extend the definition to the case of more than two classes by averaging pairwise comparisons. This measure reduces to the standard form in the two class case. We compare its properties with the standard measure of proportion correct and an alternative definition of proportion correct based on pairwise comparison of classes for a simple artificial case and illustrate its application on eight data sets. On the data sets we examined, the measures produced similar, but not identical results, reflecting the different aspects of performance that they were measuring. Like the area under the ROC curve, the measure we propose is useful in those many situations where it is impossible to give costs for the different kinds of misclassification. Homepage: http://cran.r-project.org/web/packages/HandTill2001/index.html Source Code: https://github.com/cran/HandTill2001 Dependencies: R Keywords: ROC curve; Gini index; classification rules Related Software: UCI-ml; C4.5; SMOTE; WEKA; LIBSVM; R; LeSiNN; LOF; AdaBoost.MH; rpart; PRTools; BNT; ElemStatLearn; ROCR; VQA; Grad-CAM; DeepSeeNet; CircleGAN; Vx2Text; SGAN Cited in: 69 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year A simple generalisation of the area under the ROC curve for multiple class classification problems. Zbl 1007.68180Hand, David J.; Till, Robert J. 2001 all top 5 Cited by 179 Authors 5 Hand, David J. 4 De Baets, Bernard 4 Waegeman, Willem 3 Flach, Peter A. 2 Boullart, Luc 2 Ferri, César 2 Hernández-Orallo, Jose 2 Mamitsuka, Hiroshi 1 Adams, Niall M. 1 Alabert, Aureli 1 Alarcon, Saul 1 Aryal, Sunil 1 Ballante, Elena 1 Bandos, Andriy I. 1 Bauer, Kenneth W. jun. 1 Boudriga, Noureddine A. 1 Boulesteix, Anne-Laure Isabeau 1 Bourke, Chris 1 Briggs, William M. 1 Brijs, Tom 1 Cai, Zhihua 1 Campello, Ricardo José Gabrielli Barreto 1 Cao, Fuyuan 1 Cao, Longbing 1 Carrizosa, Emilio 1 Cerquides, Jesús 1 Chang, Wenjun 1 Changming, Zhu 1 Chao, HanChieh 1 Chawla, Nitesh V. 1 Chen, Ling 1 Chen, Wei 1 Cieslak, David A. 1 Clémençon, Stéphan 1 Conde, David 1 Corazza, Marco 1 Cornelis, Chris 1 Costa, Ivan G. 1 Daqi, Gao 1 Dedene, Guido 1 Deng, Kun 1 Dong, Enming 1 Doumpos, Michael 1 Du, Bo 1 Duin, Robert P. W. 1 Edwards, Darrin C. 1 Farré, Mercè 1 Fasano, Giovanni 1 Feng, Guang 1 Feng, Qunqiang 1 Fernández-Navarro, Francisco 1 Fernández Temprano, Miguel Alejandro 1 Figini, Silvia 1 Fu, Chao 1 Funari, Stefania 1 Ganjdanesh, Alireza 1 Greiner, Russell 1 Gur, David 1 Gusso, Riccardo 1 Gutiérrez, Pedro Antonio 1 Halbersberg, Dan 1 Hamdi, Mohamed Ali 1 Hao, Shuai 1 He, Yijun 1 He, Yulin 1 Hervás-Martínez, César 1 Hoens, T. Ryan 1 Hu, Qinghua 1 Huang, Heng 1 Huang, Hsin-Hsiung 1 Huang, Jian 1 Hullermeier, Eyke 1 Ippel, L. 1 Janssens, Davy 1 Japkowicz, Nathalie 1 Jaskowiak, Pablo A. 1 Jun, Ding 1 Kamruzzaman, Md. 1 Kaptein, Maurits Clemens 1 Kaya, Hüseyin 1 Kegelmeyer, W. Philip 1 Kelly, Mark G. 1 Khan, Asifullah 1 Kim, Jaihie 1 Klawonn, Frank 1 Kwon, Oran 1 Kwong, Sam 1 Lachiche, Nicolas 1 Laine, Trevor I. 1 Lee, Sangyoun 1 Lenz, Oliver Urs 1 Lerner, Boaz 1 Li, Diana 1 Li, Jialiang 1 Li, Jianping 1 Li, Lei 1 Liang, Jiye 1 Liao, Stephen Shaoyi 1 Ling, Charles X. F. 1 Linguraru, Marius George ...and 79 more Authors all top 5 Cited in 31 Serials 10 Machine Learning 8 Pattern Recognition 5 Data Mining and Knowledge Discovery 4 Information Sciences 3 Computational Statistics and Data Analysis 2 Biometrics 2 Computers & Operations Research 2 Neural Networks 2 Journal of Machine Learning Research (JMLR) 2 Advances in Data Analysis and Classification. ADAC 1 Artificial Intelligence 1 Journal of Mathematical Psychology 1 Journal of the Operational Research Society 1 Kybernetika 1 Metron 1 Statistica Neerlandica 1 Social Choice and Welfare 1 Annals of Operations Research 1 Computational Statistics 1 Communications in Statistics. Simulation and Computation 1 European Journal of Operational Research 1 Journal of Statistical Computation and Simulation 1 Computational Optimization and Applications 1 Mathematical Methods of Operations Research 1 Journal of Applied Statistics 1 Decisions in Economics and Finance 1 Journal of Applied Mathematics 1 Statistical Applications in Genetics and Molecular Biology 1 Journal of the Korean Statistical Society 1 EURASIP Journal on Advances in Signal Processing 1 Journal of Theoretical Biology all top 5 Cited in 9 Fields 37 Computer science (68-XX) 34 Statistics (62-XX) 11 Operations research, mathematical programming (90-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Biology and other natural sciences (92-XX) 4 Numerical analysis (65-XX) 1 Combinatorics (05-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Systems theory; control (93-XX) Citations by Year