# ROC曲线

ROC分析给选择最好的模型和在上下文或者类分布中独立的抛弃一些较差的模型提供了工具.ROC分析是直接和自然的与决策的做出有相当大的关系.ROC曲线首先是由二战中的电子工程师和雷达工程师发明的,他们是用来检测战场中的敌军的,也就是信号检测理论.之后很快就被引入了心理学来进行信号的知觉检测.ROC分析现在已经在相关的领域得到了很好的发展,特别是在医学,无线电领域中,而且最近在机器学习数据挖掘领域也得到了很好的发展.

真实值
pn全部

p'

P'
n'

N'

## ROC空间

ROC空间的4个例子

ABCC'
 TP=63 FP=28 91 FN=37 TN=72 109 100 100 200
 TP=77 FP=77 154 FN=23 TN=23 46 100 100 200
 TP=24 FP=88 112 FN=76 TN=12 88 100 100 200
 TP=76 FP=12 88 FN=24 TN=88 112 100 100 200
TPR = 0.63 TPR = 0.77 TPR = 0.24 TPR = 0.76
FPR = 0.28 FPR = 0.77 FPR = 0.88 FPR = 0.12
ACC = 0.68 ACC = 0.50 ACC = 0.18 ACC = 0.82

## 参考资料

1. ^ Signal detection theory and ROC analysis in psychology and diagnostics : collected papers; Swets, 1996

### 通用参考

• X. H., Zhou. Statistical Methods in Diagnostic Medicine. Wiley & Sons. 2002. ISBN 9780471347729.

## 阅读更多

• Zou, K.H., O'Malley, A.J., Mauri, L. (2007). Receiver-operating characteristic analysis for evaluating diagnostic tests and predictive models. Circulation, 6;115(5):654–7.
• Lasko, T.A., J.G. Bhagwat, K.H. Zou and Ohno-Machado, L. (2005). The use of receiver operating characteristic curves in biomedical informatics. Journal of Biomedical Informatics, 38(5):404–415.
• Balakrishnan, N., (1991) Handbook of the Logistic Distribution, Marcel Dekker, Inc., ISBN 978-0824785871.
• Gonen M., (2007) Analyzing Receiver Operating Characteristic Curves Using SAS, SAS Press, ISBN 978-1-59994-298-1.
• Green, W.H., (2003) Econometric Analysis, fifth edition, Prentice HallISBN 0-13-066189-9.
• Heagerty, P.J., Lumley, T., Pepe, M. S. (2000) Time-dependent ROC Curves for Censored Survival Data and a Diagnostic MarkerBiometrics56:337 – 344
• Hosmer, D.W. and Lemeshow, S., (2000) Applied Logistic Regression, 2nd ed., New York; Chichester, WileyISBN 0-471-35632-8.
• Brown, C.D., and Davis, H.T. (2006) Receiver operating characteristic curves and related decision measures: a tutorial,Chemometrics and Intelligent Laboratory Systems80:24–38
• Mason, S.J. and Graham, N.E. (2002) Areas beneath the relative operating characteristics (ROC) and relative operating levels (ROL) curves: Statistical significance and interpretation. Q.J.R. Meteorol. Soc., 128:2145–2166.
• Pepe, M.S. (2003). The statistical evaluation of medical tests for classification and predictionOxfordISBN 0198565828.
• Carsten, S. Wesseling, S., Schink, T., and Jung, K. (2003) Comparison of Eight Computer Programs for Receiver-Operating Characteristic Analysis. Clinical Chemistry49:433–439
• Swets, J.A. (1995). Signal detection theory and ROC analysis in psychology and diagnostics: Collected papers. Lawrence Erlbaum Associates.
• Swets, J.A., Dawes, R., and Monahan, J. (2000) Better Decisions through Science. Scientific American, October, pages 82–87.

## 其他链接

TPR = TP / P = TP / (TP + FN)

FPR = FP / N = FP / (FP + TN)

ACC = (TP + TN) / (P + N)

SPC = TN / N = TN / (FP + TN) = 1 − FPR

PPV = TP / (TP + FP)

NPV = TN / (TN + FN)

FDR = FP / (FP + TP)
Matthews相关系数 (MCC)
$MCC = (TP*TN - FP*FN) / \sqrt{P N P' N'}$
F1评分
F1 = 2TP / (P + P')

Source: Fawcett (2006).

posted @ 2012-01-09 14:16  木lin木  阅读(9137)  评论(0编辑  收藏  举报