|
In statistics, a receiver operating characteristic (ROC), or ROC curve, is a graphical plot that illustrates the performance of a binary classifier system as its discrimination threshold is varied. The curve is created by plotting the true positive rate (TPR) against the false positive rate (FPR) at various threshold settings. The true-positive rate is also known as sensitivity or the sensitivity index ''d, known as "d-prime" in signal detection and biomedical informatics, or recall in machine learning. The false-positive rate is also known as the fall-out and can be calculated as (1 - specificity). The ROC curve is thus the sensitivity as a function of fall-out. In general, if the probability distributions for both detection and false alarm are known, the ROC curve can be generated by plotting the cumulative distribution function (area under the probability distribution from to ) of the detection probability in the y-axis versus the cumulative distribution function of the false-alarm probability in x-axis. ROC analysis provides tools to select possibly optimal models and to discard suboptimal ones independently from (and prior to specifying) the cost context or the class distribution. ROC analysis is related in a direct and natural way to cost/benefit analysis of diagnostic decision making. The ROC curve was first developed by electrical engineers and radar engineers during World War II for detecting enemy objects in battlefields and was soon introduced to psychology to account for perceptual detection of stimuli. ROC analysis since then has been used in medicine, radiology, biometrics, and other areas for many decades and is increasingly used in machine learning and data mining research. The ROC is also known as a relative operating characteristic curve, because it is a comparison of two operating characteristics (TPR and FPR) as the criterion changes.〔Swets, John A.; (''Signal detection theory and ROC analysis in psychology and diagnostics : collected papers'' ), Lawrence Erlbaum Associates, Mahwah, NJ, 1996〕 ==Basic concept== A classification model (classifier or diagnosis) is a mapping of instances between certain classes/groups. The classifier or diagnosis result can be a real value (continuous output), in which case the classifier boundary between classes must be determined by a threshold value (for instance, to determine whether a person has hypertension based on a blood pressure measure). Or it can be a discrete class label, indicating one of the classes. Let us consider a two-class prediction problem (binary classification), in which the outcomes are labeled either as positive (''p'') or negative (''n''). There are four possible outcomes from a binary classifier. If the outcome from a prediction is ''p'' and the actual value is also ''p'', then it is called a ''true positive'' (TP); however if the actual value is ''n'' then it is said to be a ''false positive'' (FP). Conversely, a ''true negative'' (TN) has occurred when both the prediction outcome and the actual value are ''n'', and ''false negative'' (FN) is when the prediction outcome is ''n'' while the actual value is ''p''. To get an appropriate example in a real-world problem, consider a diagnostic test that seeks to determine whether a person has a certain disease. A false positive in this case occurs when the person tests positive, but actually does not have the disease. A false negative, on the other hand, occurs when the person tests negative, suggesting they are healthy, when they actually do have the disease. Let us define an experiment from P positive instances and N negative instances for some condition. The four outcomes can be formulated in a 2×2 ''contingency table'' or ''confusion matrix'', as follows: 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Receiver operating characteristic」の詳細全文を読む スポンサード リンク
|