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A ROC space is defined by FPR and TPR as x and y axes, respectively, which depicts relative trade-offs between true positive (benefits) and false positive (costs). Since TPR is equivalent to sensitivity and FPR is equal to 1 − specificity , the ROC graph is sometimes called the sensitivity vs (1 − specificity) plot.
The ROC curve is created by plotting the true positive rate (TPR) against the false positive rate (FPR) at various threshold settings. An example of ROC curve and the area under the curve (AUC). The area under the ROC curve (AUC) [1] [2] is often used to summarize in a single number the diagnostic ability of the classifier. The AUC is simply ...
In a classification task, the precision for a class is the number of true positives (i.e. the number of items correctly labelled as belonging to the positive class) divided by the total number of elements labelled as belonging to the positive class (i.e. the sum of true positives and false positives, which are items incorrectly labelled as belonging to the class).
The x- and y-axes are scaled non-linearly by their standard normal deviates (or just by logarithmic transformation), yielding tradeoff curves that are more linear than ROC curves, and use most of the image area to highlight the differences of importance in the critical operating region.
Youden's index is often used in conjunction with receiver operating characteristic (ROC) analysis. [3] The index is defined for all points of an ROC curve, and the maximum value of the index may be used as a criterion for selecting the optimum cut-off point when a diagnostic test gives a numeric rather than a dichotomous result.
The relationship between sensitivity and specificity, as well as the performance of the classifier, can be visualized and studied using the Receiver Operating Characteristic (ROC) curve. In theory, sensitivity and specificity are independent in the sense that it is possible to achieve 100% in both (such as in the red/blue ball example given above).
The receiver operating characteristic (ROC) also characterizes diagnostic ability, although ROC reveals less information than the TOC. For each threshold, ROC reveals two ratios, hits/(hits + misses) and false alarms/(false alarms + correct rejections), while TOC shows the total information in the contingency table for each threshold. [2]
3 In this confusion matrix, of the 8 samples with cancer, the system judged that 2 were cancer-free, and of the 4 samples without cancer, it predicted that 1 did have cancer. All correct predictions are located in the diagonal of the table (highlighted in green), so it is easy to visually inspect the table for prediction errors, as values ...