cause these methods difficulties. Hence, the value of TNA is calculated as follows, TNA=70+90+10+15=185, and similarly TNB=80+0+5+90=175 and TNC=80+70+15+15=180. Zou, Receiver operating characteristic (roc) literature research, 2002. Therefore, if the data are balanced, the precision of the end point is PP+N=12. If the As a result the training process is For example, the false positive in class A (FPA) is calculated as follows, FPA=EBA+ECA. Given two classes, red class and blue class. This can be achieved by identifying an unknown sample by matching it with all the other known samples. This is because we only used 20 samples (a finite set of samples) in our example and a true curve can be obtained when the number of samples increased. This is can be proved simply by assuming that the negative class samples are increased by times. The outputs of classification models can be discrete as in the decision tree classifier or continuous as the Naive Bayes classifier [7]. However, they are still usually much faster to construct than The analysis of such metrics and its significance must be interpreted correctly for evaluating different learning algorithms. The values of TPR and FPR of each point/threshold are calculated in Table 1. These input patterns are called training data which are used for training the model. We find that oblique decision trees represent a good compromise To access and cite this article, please use Tharwat, A. disadvantage of neural networks is that they are notoriously slow, For plotting ROC of the class i (ci), the samples from ci represent positive samples and all the other samples are negative samples. reported some metrics which are used in medical diagnosis [20]. Generally, we can consider sensitivity and specificity as two kinds of accuracy, where the first for actual positive samples and the second for actual negative samples. J. Appl. Jaccard metric is sensitive to changes in data distributions. The nearest-neighbor method can be generalized to use the K nearest examination of an oblique decision tree to determine which parameters For decision trees, it is also possible to use known noise estimates matter) the noise in parameters as additional object features. single parameter is compared to some constant. the computation of the distance.) All of the above methods can be modified to give a probabilistic [2]R.M. Their linear combination of some or all of the parameters is computed (using The point D in the lower right corner (1,0) represents a classifier where all positive and negative samples are misclassified. For example, the accuracy is defined as follows, Acc=TP+TNTP+TN+FP+FN and the GM is defined as follows, GM=TPRTNR=TPTP+FNTNTN+FP; thus, both metrics use values from both columns of the confusion matrix. features are chosen carefully (and if they are weighted carefully in The A class represents the positive class while the B class represents the negative class. The subsequent branching until a leaf node is reached Thus, the false negative in the A class (FNA) is the sum of EAB and EAC (FNA=EAB+EAC) which indicates the sum of all class A samples that were incorrectly classified as class B or C. Simply, FN of any class which is located in a column can be calculated by adding the errors in that class/column. As I discuss below ( 3), the choice of approach intended to find a ``good-enough'' solution to the As the threshold is further reduced to be 0.8, the TPR is increased to 0.2 and the FPR remains zero.

Therefore, such these metrics cannot distinguish between the numbers of corrected labels from different classes [11]. The steps of generating ROC curve are summarized in Algorithm 1. 21 (9) (2009) 12631284. Detection Error Trade-off (DET) curve is used for evaluating biometric models. Hence, it complements the specificity as in Eq. tree, it is necessary to approximate the straight diagonal line that In other words, if the similarity score exceeds a pre-defined threshold; hence, the corresponding sample is said to be matched; otherwise, the sample is not matched. homogeneous regions where the objects are of the same classes. The original publication date for this paper was 21/08/2018. [15]C.E. [7]R.O. In axis-parallel decision and neural nets do not give much help in this process. Figure 5 shows an example of the ROC curve. A point in the ROC space is better than all other points that are in the southeast, i.e., the points that have lower TPR, higher FPR, or both (see Figure 5). Also, from the figure, it is clear that the FP area is much larger than the area of TN. This is because (1) the recall increases by increasing the threshold value and at the end point the recall reaches to the maximum recall, (2) increasing the threshold value increases both TP and FP. 10151021. One of the major disadvantages of this test is that it does not change concerning the differences between the sensitivity and specificity of the test. Thus, we can say that the closer a DET curve is to the lower left corner, the better the classification performance is. Different assessment methods are sensitive to the imbalanced data when the samples of one class in a dataset outnumber the samples of the other class(es) [25]. parameter space to a comprehensible set of parameters. A visualization of how changing the threshold changes the TP,TN,FP, and FN values. This variant represents the weighted harmonic mean between precision and recall as in Eq. In this threshold, also all negative samples are correctly classified; thus, the value of FP is still zero. Hence, we can say that the closer the PR curve is to the upper right corner, the better the classification performance is. an object belongs on the left branch or the right branch. It is straightforward through the closest object from the training set to an object being (9) [20]. are all of type 1 when x>y and are of type 2 when x0.6 where A has a slight difference (blue shaded area). For example, consider a simple The full terms of this license may be seen at http://creativecommons.org/licences/by/4.0/legalcode. In the first case which is the optimistic case, all positive samples end up at the beginning of the sequence, and this case represents the upper L segment of the rectangle in Figure 5. Thus, the specificity represents the proportion of the negative samples that were correctly classified, and the sensitivity is the proportion of the positive samples that were correctly classified. These two measures are sensitive to the imbalanced data [21,9]. An illustrative example of the AUC metric. The black circle represents a classifier that classifies the sample inside the circle as red samples (belong to the red class) and the samples outside the circle as blue samples (belong to the blue class). [17]T. Saito, M. Rehmsmeier, The precision-recall plot is more informative than the roc plot when evaluating binary classifiers on imbalanced datasets, PLoS One 10 (3) (2015) e0118432. Classification techniques have been applied to many applications in various fields of sciences. As shown in the table in Figure 6, the initial step to plot the ROC curve is to sort the samples according to their scores. (2020), Classification assessment methods, New England Journal of Entrepreneurship. On-line bibliography available from: http://splweb.bwh.harvard.edu8000. Adjusted Geometric Mean (AGM) is proposed to obtain as much information as possible about each class [11]. The publisher sincerely apologises for any inconvenience caused. The ROC curve has been used to evaluate many systems such as diagnostic systems, medical decision-making systems, and machine learning systems [26]. Balanced classification rate or balanced accuracy (BCR): this metric combines the sensitivity and specificity metrics and it is calculated as follows, BCR=12(TPR+TNR)=12(TPTP+FN+TNTN+FP).

Any classifier that has discrete outputs such as decision trees is designed to produce only a class decision, i.e., a decision for each testing sample, and hence it generates only one confusion matrix which in turn corresponds to one point into the ROC space. The algorithm requires O(nlogn) for sorting samples, and O(n) for scanning them; resulting in O(nlogn) total complexity, where n is the number of samples. The values of different classification metrics are as follows, Acc=70+8070+80+20+30=0.75,TPR=7070+30=0.7,TNR=8080+20=0.8,PPV=7070+200.78,NPV=8080+300.73,Err=1Acc=0.25,BCR=12(0.7+0.8)=0.75,FPR=10.8=0.2,FNR=10.7=0.3,Fmeasure=270(270+20+30)=0.74,OP=Acc|TPRTNR|TPR+TNR=0.75|0.70.8|0.7+0.80.683,LR+=0.710.8=3.5,LR=10.70.8=0.375,DOR=3.50.3759.33,YI=0.7+0.81=0.5, and Jaccard=7070+20+300.583. optimization problem. Technical Report PRG-TR-2-99, Oxford University Computing Laboratory, Oxford, England, 1999. 2-parameter, 2-class distribution of points with parameters x,y that Additionally, an illustrative numerical example is presented to show (1) how to calculate these measures in both binary and multi-class classification problems, and (2) the robustness of some measures against balanced and imbalanced data. The perfect classification performance in the PR curve is represented in Figure 10 by a green curve. Manage. Graphical assessment methods such as Receiver operating characteristics (ROC) and Precision-Recall curves give different interpretations of the classification performance. Also, Balance error rate (BER) or Half total error rate (HTER) represents 1BCR. You can join in the discussion by joining the community or logging in here.You can also find out more about Emerald Engage. Green regions indicate the correctly classified regions and the red regions indicate the misclassified regions. From this figure, the following remarks can be drawn. The assessment method is a key factor in evaluating the classification performance and guiding the classifier modeling. In this section, the AUC algorithm with detailed steps is explained. An unknown sample is classified to P or N. The classification model that was trained in the training phase is used to predict the true classes of unknown samples. The model is trained using input patterns and this phase is called the training phase. that a particular parameter measures the noise on another parameter. The values of precision and recall of each point/threshold are calculated in Table 1. On the other hand, in continuous output classifiers such as the Naive Bayes classifier, the output is represented by a numeric value, i.e., score, which represents the degree to which a sample belongs to a specific class. Increasing TP increases the precision while increasing the FP decreases the precision. Some of the measures which are derived from the confusion matrix for evaluating a diagnostic test are reported in [19]. (9). This metric is defined as follows: Markedness (MK): this is defined based on PPV and NPV metrics as follows, MK=PPV+NPV1 [16]. Steps 58 handle sequences of equally scored samples. (6), according to the precision metric, lowering the threshold value increases the TP or FP. However, some metrics which use values from both columns are not sensitive to the imbalanced data because the changes in the class distribution cancel each other. Hence, changing the ratio between the positive and negative classes changes that line and hence changes the classification performance. The green diagonal represents correct predictions and the pink diagonal indicates the incorrect predictions. Hence, to prevent imposter samples from being easily correctly identified by the model, the similarity score has to exceed a certain level (see Figure 11) [2]. Section 2 gives an overview of the classification assessment methods. 168-192. Moreover, based on the confusion matrix, different measures are introduced with detailed explanations. This means that more positive samples have the chance to be correctly classified; on the other hand, some negative samples are misclassified. [22]A. Srinivasan, Note on the location of optimal classifiers in n-dimensional roc space. A basic ROC curve showing important points, and the optimistic, pessimistic and expected ROC segments for equally scored samples. From Figure 7 it is clear that the ROC curve is a step function. This metric is sensitive to imbalanced data. Therefore, the Area under the ROC curve (AUC) metric is used to calculate the area under the ROC curve. As shown in Figure 6, the threshold value is set at maximum (t1=); hence, all samples are classified as negative samples and the values of FPR and TPR are zeros and the position of t1 is in the lower left corner (the point (0,0)). Hassanien, Chaotic antlion algorithm for parameter optimization of support vector machine, Appl. These results reflect how the precision and accuracy metrics are sensitive to the imbalanced data as mentioned in Section 2.1. However, two classifiers with two different ROC curves may have the same AUC score. The algorithm scans all samples and the value of TP is increased for each positive sample while the value of FP is increased for each negative sample. The goal of a learning algorithm is to learn from the training data to predict class labels for unseen data; this is in the testing phase. The biggest advantage of neural network methods is that they are After a series of In this section, two examples are introduced. (There are some thinning methods that can be used on the (2) [20]. Accordingly, it is a fact that however the classification threshold is perfectly chosen, some classification errors occur. The F-measures used only three of the four elements of the confusion matrix and hence two classifiers with different TNR values may have the same F-score. In other words, it is the proportion of the negative samples that were incorrectly classified. [20]M. Sokolova, N. Japkowicz, S. Szpakowicz, Beyond accuracy, f-score and roc: a family of discriminant measures for performance evaluation, in: Australasian Joint Conference on Artificial Intelligence, Springer, 2006, pp. [25]A. Tharwat, Y.S. This overview starts by highlighting the definition of the confusion matrix in binary and multi-class classification problems. More details about these two metrics are in Section 2.8. determined into what classes an object may be categorized and also has The t3: The threshold value decreased as shown in Figure 8b) and as shown there are two positive samples are correctly classified. There are In that paper, only eight measures were introduced. In biometric systems, a single threshold separates the two groups of scores; thus, it can be utilized for differentiating between clients and imposters. As shown, the AUC of B classifier is greater than A; hence, it achieves better performance. shortcoming of nearest neighbor methods is that they are very sensitive [4]A.P. t11: This is an important threshold value where the numbers of errors from both positive and negative classes are equal (see Figure 8(d)) TP=TN=6 and FP=FN=4). (2) [20]. Moreover, the gray shaded area is common in both classifiers, while the red shaded area represents the area where the B classifier outperforms the A classifier.