roc auc imbalanced data

PubMed Central Combinations of positive and negative score distributions generate five different levels for the simulation analysis. AUC Maximization for Low-Resource Named Entity Recognition. We explain this in detail below. CC is considerably different from the other ROC variants in terms of the interpretation of the plot. The ROC plots are unchanged between balanced and imbalanced datasets (Fig. 2003;59(3):61423. which averaging should be used when computing the ROC AUC on imbalanced Lamont Primary Health Care Research Centre and Bruere Research Institute, Ottawa, Canada, Division of Clinical Public Health, Dalla Lana School of Public Health, Toronto, Canada, You can also search for this author in So an AUC which is close to 1 is quite often considered to be a confirmation of the model being good. Asking for help, clarification, or responding to other answers. The authors would like to thank members of the Computational Biology Unit (CBU) at the University of Bergen for commenting on earlier versions of the manuscript. 2015;68(8):8559. Three obvious approaches to make a ROC curve from these ties are to use the upper bound with positive calculation first (6812 in Fig. where P is the total number of positives, which is equal to the sum of true positives (TP) and false negatives (FN). For tied scores, we assigned ranks in order of occurrence in the original array. Thompson ML, Zucchini W. On the statistical analysis of ROC curves. The AUC (ROC) scores are in good agreement with the visual impression of the ROC plot, but likewise fail in terms of interpretability with respect to their practical meaning. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Instances excluded by filtering likely have no scores assigned. The ability of a classifier or diagnostic test to discriminate between actual positives and negatives, is often assessed by its curve in a receiver-operator characteristic (ROC) plot and the area under the ROC curve (AUC).However, when data are imbalanced with few positives relative to negatives (i.e. Supplementary References. The second label, Literature analysis, represents an analysis of the results from two sets of PubMed search to investigate the actual usage of evaluation measures in the life science literature. 2B). Fawcett T. An introduction to ROC analysis. We used the Data type category to identify whether the data set used for performance evaluation is imbalanced. You will work with the Credit Card Fraud Detection dataset hosted on Kaggle. CSquotes package displays a [?] One complexity with the dual perspective of the concordant partial AUC is that a range along one axis, either the x axis (FPR) or the y axis (TPR), does not uniquely specify a partial curve for a classifier. In our comprehensive study, we show the differences between the various measures from several perspectives. The goal of the second analysis was to make a selection of binary-classification studies with imbalanced datasets for a further analysis. Notably, AUC could be computed as half the horizontal integral and vertical integral, but the AUC is a special case where those two integrals and areas are necessarily equal, and where average TPR and average TNR are necessarily equal [11]. Citation: Saito T, Rehmsmeier M (2015) The Precision-Recall Plot Is More Informative than the ROC Plot When Evaluating Binary Classifiers on Imbalanced Datasets. Proc Natl Acad Sci. 7B indicates that all classifiers have a very good to excellent prediction performance. Overall, a combination of AUCCalculator and any graph plotting program can be recommended for the creation of accurate PRC plots. To learn more, see our tips on writing great answers. The higher the AUC, the closer the classifier is to being perfect in classifying actual positives and negatives at one threshold at or toward the top left corner. Alternative measures such as positive predictive value (PPV) and the associated Precision/Recall (PRC) plots are used less frequently. More importantly, these unchanged measures fail to capture the poor performance of the classifier for the imbalanced sample. It usually divides a training dataset further into training and validation subsets, for example for cross-validation [21]. broad scope, and wide readership a perfect fit for your research every time. Positives are candidate genes that overlap with the actual miRNA genes from miRBase. We then started again from the data sampling for another round. Radiology. A: C-D in S1 File), which are additionally unintuitive without a good understanding of NE[C] and PCF (+). The top-performing classifiers, MiRFinder and miPred, have similar ROC curves, but miPred appears to perform better than MiRFinder in the early-retrieval area. How to Calibrate Probabilities for Imbalanced Classification A viewer might be tempted to be happy about the mid-FPR-field performance, not realizing that because of the strong imbalance of the data these FPRs could translate into large numbers of false-positive predictions. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. This is because ROC AUC only tells the property of two conditional distribution \(p(score|y = 1)\) and \(p(score|y = 0)\) but has nothing to do with the number of samples in each category. Ozenne B, Subtil F, Maucort-Boulch D. The precisionrecall curve overcame the optimism of the receiver operating characteristic curve in rare diseases. The upper barplot shows the number of papers found by the term ROC, whereas the lower plot shows the number found by the term ((Support Vector Machine) AND Genome-wide) NOT Association. What are these planes and what are they doing? Summary of the re-evaluation. Table G in S1 File. 0.5 but a very low FPR (<0.05). Acad Radiol. However, sometimes, it is more appropriate to evaluate your classifier based on measuring the urve (AUPRC). No specific funding was sought or allocated for this specific paper or work.. Ottawa Hospital Research Institute, Ottawa, K1H 8L6, Canada, Faculty of Engineering, University of Waterloo, Waterloo, N2L 3G1, Canada, Holzinger Group (HCAI), Institute for Medical Informatics/Statistics, Medical University Graz, 8036, Graz, Austria, Institute of Interactive Systems and Data Science, Graz University of Technology, 8010, Graz, Austria, School of Public Health and Health Systems, University of Waterloo, Waterloo, N2L 3G1, Canada, Universidad ORT Uruguay, 11100, Montevideo, Uruguay, Department of Family Medicine, University of Ottawa, Ottawa, Canada, School of Epidemiology, Public Health and Preventive Medicine, University of Ottawa, Ottawa, Canada, Institute for Clinical Evaluative Sciences, Ottawa, Canada, C.T. Stat Med. 1997;30:114559. The null hypothesis is that two group has the same mean. PCF (+) is based on the probability of correctly classifying positives, and it is calculated by class probabilities and misclassification costs [5]. PubMedGoogle Scholar. AUC (PRC) scores (Table 5) agree with the PRC plot in their ranking of the candidates, but, again naturally, cannot capture the variation of MiRFinder performance over the range of recovery rates. The partial area under the summary ROC curve. Similar to the ROC plot in Fig. The PRC plot in Fig. PRC plots show the practically relevant measures, precision and recall, of which precision is particularly important because it measures the fraction of correct predictions among the positive predictions. Three main and 13 sub groups categorize the 58 research papers found by PubMed search. The parameter average="weighted" should account for imbalance. 2 Interpreting AUC, accuracy and f1-score on the unbalanced dataset. A comparison of the leftmost partial curve and area between two classifiers applied to Ljubljana breast cancer remission data. The re-analysis used two independent test sets, T1 and T2. Hanley JA, Hajian-Tilaki KO. Tang Y, Zhang Y-Q, Chawla NV, Krasser S. Svms modeling for highly imbalanced classification. The simulations use randomly generated samples with different performance levels. Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach. 2A). Is it meaningful if I have imbalanced data? We used the Evaluation method category to identify what methods are used to evaluate the classification models. Once the PCF (+) value of interest is determined, it is easy to compare the performances of multiple classifiers. Classifiers sometimes fail to give scores to parts of the prediction. However, it requires special caution when used with imbalanced datasets. (C) Two ovals show examples of TPs, FPs, TNs, and FNs for balanced (left) and imbalanced (right) data. Epidemiology. 5D) indicate that 75% and 25% are correct positive predictions in the balanced and in the imbalanced case, respectively, and these correct positive predictions are 50% of all positives. 5A), and all AUC (ROC) scores are unhanged accordingly (Table E in S1 File). Another common metric is AUC, area under the receiver operating characteristic ( ROC) curve. 2012;12(1):82. Pattern Recogn Lett. They have been successfully applied to a wide range of biological and medical problems in recent years [13]. A new concordant partial AUC and partial c statistic for imbalanced How to choose between ROC AUC and F1 score? - Cross Validated All these measures have different advantages and disadvantages. We then calculated the scores of the tools on T1 and T2 (see Supplementary Methods in S1 File for more details on test data and score calculations). Stat Methods Med Res. For instance, we have y = 0.5 for a balanced class distribution, but y = 0.09 for an imbalanced class distribution in which the ratio of P:N is 1:10 (see Fig. Stat Methods Med Res. Consider running the example a few times and compare the average outcome. Phys Med Biol. PhD thesis, The University of Queensland. 1984;4(2):13750. 2011;30(10):110517. In case of static data, the area under the receiver operating characteristics . Is ROC AUC good for Imbalanced Data? - ProfoundAdvice This is because a small number of correct or incorrect predictions can result in a large change in the ROC Curve or ROC AUC score. Only PRC changes with the ratio of positives and negatives. Based on recent advances in area under the ROC curve (AUC) maximization, we propose to optimize the NER model by maximizing the AUC score. The first label, ROC, represents the theoretical background of basic measures, ROC, and ROC alternatives except PRC. 2A) is useful for evaluating a fraction of the data with high-ranked instances [36, 37]. PLoS One. 2014;35(29):192531. if the model just guessed =0 it would also achieve a ROC-AUC score of 0.67. Suppose the task is to detect dementia from speech, and 99% of people don't have dementia and only 1% do. Two points of ER- (red dots with black circle in Fig. PCF (+) is based on the probability of correctly classifying positives, whereas NE[C] represents the classification performance (see Supplementary Methods in S1 File for the PCF(+) and NE[C] calculations). Google Scholar. Operating points are based on class probabilities and misclassification costs. and ROC-AUC metric from above example is 0.979. Metz CE, Kronman HB. 1986;1986:1041. AP (or AUPRC) is thought to be a good measure for imbalanced data, preferred over AUC [45, 46], and it is more popular measure than pAUC. 7D reveals the bitter truth. Alternative to 'stuff' in "with regard to administrative or financial _______.". . Assessing the performance of prediction models: a framework for some traditional and novel measures. The original MiRFinder study evaluates seven additional tools (Table G in S1 File). 1 Answer Sorted by: 4 You are actually asking three separate questions: Why is ROC AUC and Balanced Accuracy so high? From the simulation you can see, if the feature space does not have enough distinguish power, the linear classifier will behave poorly (in term of ROC AUC) no matter whether the data set is imbalanced or not But it is good to note that imbalanced data set gives some misleadingly good results. The results of the simulations suggest that the interpretation of the ROC plot requires a special caution when the data are imbalanced and the early retrieval area needs to be checked. Fig. Descriptions of the three main and 13 sub categories. A new concordant partial AUC and partial c statistic for imbalanced data in the evaluation of machine learning algorithms, BMC Medical Informatics and Decision Making, $$ pAUC\triangleq {\int}_{x_1}^{x_2}r(x) dx $$, $$ {pAUC}_x\triangleq {\int}_{y_1}^{y_2}1-{r}^{-1}(y) dy $$, $$ c\triangleq \frac{1}{PN}\sum \limits_{j=1}^P\sum \limits_{k=1}^NH\left(g\left({p}_j\right)-g\left({n}_k\right)\right) $$, \( \left\{{p}_{1\dots J}^{\prime}\right\} \), \( \left\{{n}_{1\dots K}^{\prime}\right\} \), $$ \mathrm{simple}\ {c}_{\Delta }\triangleq \frac{1}{2 JN}\sum \limits_{j=1}^J\sum \limits_{k=1}^NH\left(g\left({p}_j^{\prime}\right)-g\left({n}_k\right)\right)+\frac{1}{2 PK}\sum \limits_{j=1}^P\sum \limits_{k=1}^KH\left(g\left({p}_j\right)-g\left({n}_k^{\prime}\right)\right) $$, $$ {\overset{\sim }{c}}_{\Delta }\triangleq \frac{2 PN\cdotp {c}_{\Delta }}{J\cdotp N+K\cdotp P} $$, $$ c=\sum \limits_{i=1}^q{\left({c}_{\Delta }\right)}_i $$, \( {\underset{\_}{w}}^{+}=\left[{w}_q\right],\forall q \), \( {\underset{\_}{w}}^{-}=\left[{w}_r\right],\forall r \), $$ {\displaystyle \begin{array}{c}{c}_{\varDelta}\triangleq \frac{1}{2N{\sum}_{q=1}^J{w}_q^{+}}\sum \limits_{j=1}^J\sum \limits_{k=1}^N{w}_j^{+}\cdot H\left(g\left({p}_j^{\prime}\right)-g\left({n}_k\right)\right)\\ {}+\frac{1}{2P{\sum}_{r=1}^K{w}_r^{-}}{\sum}_{j=1}^P{\sum}_k^K{w}_k^{-}\cdot H\left(g\left({p}_j\right)-g\left({n}_k^{\prime}\right)\right)\end{array}} $$, $$ {pAUC}_c\triangleq \frac{1}{2} pAUC+\frac{1}{2}{pAUC}_x $$, $$ =\frac{1}{2}{\int}_{x_1}^{x_2}r(x) dx+\frac{1}{2}{\int}_{y_1}^{y_2}1-{r}^{-1}(y) dy $$, $$ AUC=c=\sum \limits_{i=1}^q{\left({pAUC}_c\right)}_i $$, $$ {\left({pAUC}_c\right)}_i={\left({c}_{\Delta }\right)}_i $$, https://doi.org/10.1186/s12911-019-1014-6, https://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+, https://archive.ics.uci.edu/ml/datasets/breast+cancer}, https://doi.org/10.1016/j.patrec.2005.10.010, https://doi.org/10.1097/ede.0b013e3181c30fb2, https://doi.org/10.1111/j.1466-8238.2007.00358.x, https://doi.org/10.1016/j.acra.2012.09.004, https://doi.org/10.1148/radiology.201.3.8939225, https://doi.org/10.1371/journal.pone.0118432, http://creativecommons.org/licenses/by/4.0/, http://creativecommons.org/publicdomain/zero/1.0/, Explainable AI in Medical Informatics and Decision Support, bmcmedicalinformaticsanddecisionmaking@biomedcentral.com. A Gentle Introduction to Threshold-Moving for Imbalanced Classification However that might not be the case as we will see. AUC (PRC) scores (Table 5) agree with the order of performance established in the PRC plot, but, being summaries of whole curves, cannot express the change of performance over the range of recall values. The scripts also include graph-plotting capability. Integration of multicriteria decision analysis in gis to develop land suitability for agriculture: application to durum wheat cultivation in the region of mleta in Algeria. rev2023.6.28.43515. Stated that way, it's clear that a classifier that predicts random probabilities for every instance will have 0.5 AUC, regardless of class balance. https://doi.org/10.1371/journal.pone.0118432. Interpolation between two points A and B in PRC space can be represented as a function y = (TPA + x) / {TPA + x + FPA + ((FPB - FPA) * x) / (TPB - TPA)} where x can be any value between TPA and TPB [26]. Python Machine Learning - AUC - ROC Curve - W3Schools Dua, D., Graff, C.: UCI machine learning repository (2017). Its results show that PR AUC is more informative than ROC AUC when the data is imbalanced. Why are ROC curves better for imbalanced datasets? But lets take a look at an example of a dataset which could give rise to this excellent ROC curve, while the underlying classifier being of poor quality. '90s space prison escape movie with freezing trap scene. Hilden J. Article https://doi.org/10.1093/eurheartj/ehu207 arXiv:1011.1669v3. From the results we collected the annual number of articles between 2002 and 2012. Login to access subscriber-only resources. How to calculate roc auc score for the whole epoch like avg accuracy? Uno H, Cai T, Pencina MJ, DAgostino RB, Wei L. On the c-statistics for evaluating overall adequacy of risk prediction procedures with censored survival data. CA Cancer J Clin. Sensitivity (SN) and specificity (SP) are also popular [31]. 1B). These equalities were validated in all four data sets. PRC plots express the susceptibility of classifiers to imbalanced datasets with clear visual cues. I have a binary response variable (label) in a dataset with around 50,000 observations. Discover a faster, simpler path to publishing in a high-quality journal. It is model-wide because it shows pairs of specificity and sensitivity values calculated at all possible threshold scores. The area under the ROC curve (AUC) can be interpreted as the probability that the classification model correctly ranks a random positive example higher than a random negative example. auc - How much is ROC biased towards the minority class - Cross The model-wide evaluation measures we analyse in our study are ROC, PRC, CROC, and CC. We have shown here that, unlike ROC plots, PRC plots express the susceptibility of classifiers to imbalanced datasets with clear visual cues and allow for an accurate and intuitive interpretation of practical classifier performance. To investigate what evaluation measures are used for binary classifiers in life science studies, we performed two PubMed searches. The cofounder of Chef is cooking up a less painful DevOps (Ep. We subsequently ranked them from the lowest to the highest scores. Walter SD. The use of the area under the ROC curve in the evaluation of machine learning algorithms. https://doi.org/10.1111/j.1466-8238.2007.00358.x. Signal Detection Theory and Psychophysics, vol. 1 keras: Assessing the ROC AUC of multiclass CNN. Which F1 score is appropriate for imbalanced classification? Similar to ROC, the CROC curves fail to explicitly show this performance difference. Mendas A, Delali A. 1C). The measures we discuss in this study are accuracy (ACC), error rate (ERR), sensitivity (SN), specificity (SP), true positive rate (TPR), recall (REC), false positive rate (FPR), precision (PREC), positive predictive value (PPV), Matthews correlation coefficient (MCC) [32], and F score [33] where is 0.5, 1, or 2. A re-analysis of the MiRFinder study reveals that PRC is stronger than ROC on imbalanced data. With imbalanced classes, it's easy to get a high accuracy without actually making useful predictions. Binary classifiers are routinely evaluated with performance measures such as sensitivity and specificity, and performance is frequently illustrated with Receiver Operating Characteristics (ROC) plots. A black line represents a classifier that separates the data into predicted as positive indicated by the upward arrow P and predicted as negative indicated by the downward arrow N. While any such threshold, which divides a dataset into positively and negatively predicted classes, can be reasonable in a particular application, it is not obvious how the right threshold value should be chosen. This removes monotonic behaviour, but the subtraction which is related to Kappa and AUK, diverges from the meaning of AUC and concordance. Hence, it is practical to check the performance of the early retrievals, which only examines a limited number of top-scoring instances. PubMed We used the PubMed term ((Support Vector Machine) AND Genome-wide) NOT Association to find studies with imbalanced datasets that use support vector machines (SVMs) [51] for classification. However, this is not true for the normalized partial AUC (\( \overset{\sim }{pAUC} \)) when comparing different partial curves for the same classifier (Table3) because it monotonically increases with FPR. A number of tools for making ROC and PRC plots are freely available, but PRC functionality is generally deficient in comparison with ROC functionality. 2019;28(1):18495. Hence, precision reveals differences in performance that go unnoticed when using accuracy. By using this website, you agree to our The ROC curve is simply a graphical plot of the relationship between the False Positive Rate (FPR) and the True Positive Rate (TPR) when the discrimination threshold of a classifier is varied. 2A), the lower bound with negative calculation first (61012 in Fig. The results of our evaluations are shown in Fig. Land management with gis and multicriteria analysis. The AUC (ROC) scores (Table 5) indicate that MiRFinder is slightly better than miPred when studied over the whole range of FPRs, but this difference is too small to be of any practical relevance. If we take the sum of pAUCc measures for any set of partial curves which span the whole ROC curve and which are not overlapping, they sum to the AUC and c statistic. 1997;4(1):4958. Stat Med. Alternative to 'stuff' in "with regard to administrative or financial _______.". The authors declare that they have no competing interests. ROC Curves and Precision-Recall Curves for Imbalanced Classification - MachineLearningMastery.com Most imbalanced classification problems involve two classes: a negative case with the majority of examples and a positive case with a minority of examples. Balanced Accuracy: When Should You Use It? - neptune.ai If the false labeled samples dominate the likelihood function (or loss function), the model will mainly work on decrease the likelihood or that part and does little on true labeled samples. Our literature analysis suggests that the majority of such studies work with imbalanced datasets and use ROC as their main performance evaluation method. Why is Average Precision and F1 score so low? The thresholds are different probability cutoffs that separate the two classes in binary . Then you can submit a classifier that always outputs "no dementia", and that would achieve 99% accuracy. Nguyen, N. D., Tan, W., Du, L., Buntine, W., Beare, R., & Chen, C. (2023). When we move the boundary-threshold from right to left we classify more data points as positive, increasing the number of false positives and true positives, giving rise to the ROC curve previously shown above. Guessing all points as a single class is represented in ROC space as the top-right or bottom-left corner, and doesn't give much information about the AUC. With the rapid expansion of high-throughput sequencing technology, the number of studies with machine leaning methods will likely increase. By clicking Post Your Answer, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct. Hence McClish [17] proposes the standardized Partial Area (sPA). Misclassification costs are often unknown but can for example be estimated from the class distributions. Basic evaluation measures from the confusion matrix. We also proposed a partial c statistic and concordance matrix which shed light on the meaning of partial areas. Handling Class Imbalance with R and Caret - Wicked Good Data Another measure is precision (PREC), and PRC is based on it. 2000;7(1):6778. Cost curves are useful when the testing of various misclassification costs and class probabilities is required, but a good understanding of PCF(+) and NE[C] is mandatory. The first label, Simulation, represents a simulation analysis with randomly generated samples for ROC, CROC, CC, and PRC. If the problem is highly imbalanced, balanced accuracy is a better choice than ROC_AUC since ROC_AUC is problematic with imbalanced data i.e when skewness is severe, because a small number of correct/incorrect predictions can lead to a great change in the score. The ROC curve is defined by varying a decision threshold, and so requires a probability or other confidence measure, not just a hard prediction. Three practical examples of ROC characteristics that associate with interpolation are ROC convex hull [39], the treatment of ties, and default values for missing scores. Score distributions of positives and negatives for the performance simulations. PubMed Conceived and designed the experiments: TS MR. Precision is a direct and intuitive measure of this aspect of performance. Table A in S1 File. What are the benefits of not using private military companies (PMCs) as China did? T1 contains 819 positives and 11 060 negatives, and T2 contains 111 positives and 13 444 negatives. sPA subtracts any area under the major diagonal (considered non-informative) and then standardizes the result to the range [0.5, 1]. Steyerberg EW. Anyone you share the following link with will be able to read this content: Sorry, a shareable link is not currently available for this article. This is essentially the probability that your classifier gives you a false alarm, and it is defined as follows: where N is the total number of negatives, which is equal to the sum of false positives (FP) and true negatives (TN). The majority of recent machine-learning libraries can produce discriminant values or posterior probabilities that can be used as scores [27, 34, 35], but not all classifiers provide such values. ROC is a popular and strong measure to evaluate the performance of binary classifiers. Nonetheless, care must be taken when interpolations between points are performed, since the interpolation methods for PRC and ROC curves differROC analysis uses linear and PRC analysis uses non-linear interpolation. skinny inner tube for 650b (38-584) tire? Our experimental method has two steps: first, we validate expected equalities among measures on four data sets; then, we validate the behaviour of measures as inequal- ities. In the second PubMed search, we aimed to find genome-wide studies with Support Vector Machine classifiers and used the term ((Support Vector Machine) AND Genome-wide) NOT Association. Springer. Therefore, CROC can be useful when comparing the performance of classifiers in the early retrieval area. However, the NN curve goes up more quickly in the middle (FPR1.5) and has more green area. 2008;6917(69170):69170. https://doi.org/10.1117/12.769888. on a model's ROC curve, while AUC measures all operating points. Privacy Table 4 shows that differences between neural network (NN) and support vector machine (SVM) classifiers (NN-SVM) in partial areas sum to the difference between the AUC. Five curves represent five different performance levels: Random (Rand; red), Poor early retrieval (ER-; blue), Good early retrieval (ER+; green), Excellent (Excel; purple), and Perfect (Perf; orange). A CROC plot is constructed with a magnifier function that transforms the FPRs on the x-axis. For T2, the RNAz tool was used to generate miRNA gene candidates. CROC, CC, and PRC have been suggested as alternatives to ROC, but are less frequently used. All of these measures are single-threshold measures, that is, they are defined for individual score thresholds (cutoffs) of a classifier and cannot give an overview of the range of performance with varying thresholds. 2A). . 7 and Table 5 and are described and discussed in the following sub-sections. Although interpolation in PRC analysis requires more calculations than in ROC analysis, it is nonetheless critical to follow the correct procedure if misleading plots are to be avoided, especially when the distance of PRC points to be interpolated between is very large. We calculated basic evaluation measures from a confusion matrix. PF and DM provided assistance on theory and general edits, while DM and HQ provided clinical context and interpretation and helped select the data set. McClish DK. Another potential problem is that AUC (ROC) can be inaccurate for fair comparisons when two ROC curves are crossing each other. . This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Through the Theoretical Background section, we review the performance measures including basic measures from the confusion matrix and threshold-free measures such as ROC and PRC. CROC and CC. 2018;27(8):235973. For instance, the AUC (PRC) of random classifiers is 0.5 only for balanced class distributions, whereas it is P / (P + N) for the general case, including balanced and imbalanced distributions.
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