The use of the area under the ROC curve in the evaluation of machine learning algorithms
TL;DR: AUC exhibits a number of desirable properties when compared to overall accuracy: increased sensitivity in Analysis of Variance (ANOVA) tests; a standard error that decreased as both AUC and the number of test samples increased; decision threshold independent; and it is invariant to a priori class probabilities.
Abstract: In this paper we investigate the use of the area under the receiver operating characteristic (ROC) curve (AUC) as a performance measure for machine learning algorithms. As a case study we evaluate six machine learning algorithms (C4.5, Multiscale Classifier, Perceptron, Multi-layer Perceptron, k-Nearest Neighbours, and a Quadratic Discriminant Function) on six ''real world'' medical diagnostics data sets. We compare and discuss the use of AUC to the more conventional overall accuracy and find that AUC exhibits a number of desirable properties when compared to overall accuracy: increased sensitivity in Analysis of Variance (ANOVA) tests; a standard error that decreased as both AUC and the number of test samples increased; decision threshold independent; and it is invariant to a priori class probabilities. The paper concludes with the recommendation that AUC be used in preference to overall accuracy for ''single number'' evaluation of machine learning algorithms.
Summary (1 min read)
Jump to: [Summary] and [C and Multiscale Classi er two neural networks Perceptron and Multi layer Perceptron]
Summary
- In this paper the authors investigate the use of receiver operating characteristic ROC curve for the evaluation of machine learning algorithms.
- In particular the authors investigate the use of the area under the ROC curve AUC as a measure of classi er performance.
- The machine learning algorithms used are chosen to be representative of those in common use two decision trees.
C and Multiscale Classi er two neural networks Perceptron and Multi layer Perceptron
- And two statistical methods K Nearest Neighbours and a Quadratic Discriminant Function.
- The evaluation is done using six real world medical diagnostics data sets that contain a varying numbers of inputs and samples but are primarily continuous input binary classi cation problems.
- The authors identify three forms of bias that can a ect comparisons of this type estimation selection and expert bias and detail the methods used to avoid them.
- The authors use this equivalence to show that the standard deviation of AUC estimated using fold cross validation is a reliable estimator of the standard error estimated using the Wilcoxon test.
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Citations
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TL;DR: In this article, a method of over-sampling the minority class involves creating synthetic minority class examples, which is evaluated using the area under the Receiver Operating Characteristic curve (AUC) and the ROC convex hull strategy.
Abstract: An approach to the construction of classifiers from imbalanced datasets is described. A dataset is imbalanced if the classification categories are not approximately equally represented. Often real-world data sets are predominately composed of "normal" examples with only a small percentage of "abnormal" or "interesting" examples. It is also the case that the cost of misclassifying an abnormal (interesting) example as a normal example is often much higher than the cost of the reverse error. Under-sampling of the majority (normal) class has been proposed as a good means of increasing the sensitivity of a classifier to the minority class. This paper shows that a combination of our method of oversampling the minority (abnormal)cla ss and under-sampling the majority (normal) class can achieve better classifier performance (in ROC space)tha n only under-sampling the majority class. This paper also shows that a combination of our method of over-sampling the minority class and under-sampling the majority class can achieve better classifier performance (in ROC space)t han varying the loss ratios in Ripper or class priors in Naive Bayes. Our method of over-sampling the minority class involves creating synthetic minority class examples. Experiments are performed using C4.5, Ripper and a Naive Bayes classifier. The method is evaluated using the area under the Receiver Operating Characteristic curve (AUC)and the ROC convex hull strategy.
17,313 citations
TL;DR: The purpose of this article is to serve as an introduction to ROC graphs and as a guide for using them in research.
Abstract: Receiver operating characteristics (ROC) graphs are useful for organizing classifiers and visualizing their performance. ROC graphs are commonly used in medical decision making, and in recent years have been used increasingly in machine learning and data mining research. Although ROC graphs are apparently simple, there are some common misconceptions and pitfalls when using them in practice. The purpose of this article is to serve as an introduction to ROC graphs and as a guide for using them in research.
17,017 citations
Cites methods from "The use of the area under the ROC c..."
...A common method is to calculate the area under the ROC curve, abbreviated AUC (Bradley, 1997; Hanley and McNeil, 1982)....
[...]
TL;DR: In this article, a method of over-sampling the minority class involves creating synthetic minority class examples, which is evaluated using the area under the Receiver Operating Characteristic curve (AUC) and the ROC convex hull strategy.
Abstract: An approach to the construction of classifiers from imbalanced datasets is described. A dataset is imbalanced if the classification categories are not approximately equally represented. Often real-world data sets are predominately composed of "normal" examples with only a small percentage of "abnormal" or "interesting" examples. It is also the case that the cost of misclassifying an abnormal (interesting) example as a normal example is often much higher than the cost of the reverse error. Under-sampling of the majority (normal) class has been proposed as a good means of increasing the sensitivity of a classifier to the minority class. This paper shows that a combination of our method of over-sampling the minority (abnormal) class and under-sampling the majority (normal) class can achieve better classifier performance (in ROC space) than only under-sampling the majority class. This paper also shows that a combination of our method of over-sampling the minority class and under-sampling the majority class can achieve better classifier performance (in ROC space) than varying the loss ratios in Ripper or class priors in Naive Bayes. Our method of over-sampling the minority class involves creating synthetic minority class examples. Experiments are performed using C4.5, Ripper and a Naive Bayes classifier. The method is evaluated using the area under the Receiver Operating Characteristic curve (AUC) and the ROC convex hull strategy.
11,512 citations
25 Jun 2006
TL;DR: It is shown that a deep connection exists between ROC space and PR space, such that a curve dominates in R OC space if and only if it dominates in PR space.
Abstract: Receiver Operator Characteristic (ROC) curves are commonly used to present results for binary decision problems in machine learning. However, when dealing with highly skewed datasets, Precision-Recall (PR) curves give a more informative picture of an algorithm's performance. We show that a deep connection exists between ROC space and PR space, such that a curve dominates in ROC space if and only if it dominates in PR space. A corollary is the notion of an achievable PR curve, which has properties much like the convex hull in ROC space; we show an efficient algorithm for computing this curve. Finally, we also note differences in the two types of curves are significant for algorithm design. For example, in PR space it is incorrect to linearly interpolate between points. Furthermore, algorithms that optimize the area under the ROC curve are not guaranteed to optimize the area under the PR curve.
5,063 citations
Cites methods from "The use of the area under the ROC c..."
...Often, the area under the curve is used as a simple metric to define how an algorithm performs over the whole space (Bradley, 1997; Davis et al., 2005; Goadrich et al., 2004; Kok & Domingos, 2005; Macskassy & Provost, 2005; Singla & Domingos, 2005)....
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23 Aug 2005
TL;DR: Two new minority over-sampling methods are presented, borderline- SMOTE1 and borderline-SMOTE2, in which only the minority examples near the borderline are over- Sampling, which achieve better TP rate and F-value than SMOTE and random over-Sampling methods.
Abstract: In recent years, mining with imbalanced data sets receives more and more attentions in both theoretical and practical aspects. This paper introduces the importance of imbalanced data sets and their broad application domains in data mining, and then summarizes the evaluation metrics and the existing methods to evaluate and solve the imbalance problem. Synthetic minority over-sampling technique (SMOTE) is one of the over-sampling methods addressing this problem. Based on SMOTE method, this paper presents two new minority over-sampling methods, borderline-SMOTE1 and borderline-SMOTE2, in which only the minority examples near the borderline are over-sampled. For the minority class, experiments show that our approaches achieve better TP rate and F-value than SMOTE and random over-sampling methods.
2,800 citations
Cites background from "The use of the area under the ROC c..."
...ROC curve [9] is one of the popular metrics to evaluate the learners for imbalanced data sets....
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...AUC (Area under ROC) can also be applied to evaluate the imbalanced data sets [9]....
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References
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21,694 citations
Book•
15 Oct 1992TL;DR: A complete guide to the C4.5 system as implemented in C for the UNIX environment, which starts from simple core learning methods and shows how they can be elaborated and extended to deal with typical problems such as missing data and over hitting.
Abstract: From the Publisher:
Classifier systems play a major role in machine learning and knowledge-based systems, and Ross Quinlan's work on ID3 and C4.5 is widely acknowledged to have made some of the most significant contributions to their development. This book is a complete guide to the C4.5 system as implemented in C for the UNIX environment. It contains a comprehensive guide to the system's use , the source code (about 8,800 lines), and implementation notes. The source code and sample datasets are also available on a 3.5-inch floppy diskette for a Sun workstation.
C4.5 starts with large sets of cases belonging to known classes. The cases, described by any mixture of nominal and numeric properties, are scrutinized for patterns that allow the classes to be reliably discriminated. These patterns are then expressed as models, in the form of decision trees or sets of if-then rules, that can be used to classify new cases, with emphasis on making the models understandable as well as accurate. The system has been applied successfully to tasks involving tens of thousands of cases described by hundreds of properties. The book starts from simple core learning methods and shows how they can be elaborated and extended to deal with typical problems such as missing data and over hitting. Advantages and disadvantages of the C4.5 approach are discussed and illustrated with several case studies.
This book and software should be of interest to developers of classification-based intelligent systems and to students in machine learning and expert systems courses.
21,674 citations
TL;DR: A representation and interpretation of the area under a receiver operating characteristic (ROC) curve obtained by the "rating" method, or by mathematical predictions based on patient characteristics, is presented and it is shown that in such a setting the area represents the probability that a randomly chosen diseased subject is (correctly) rated or ranked with greater suspicion than a random chosen non-diseased subject.
Abstract: A representation and interpretation of the area under a receiver operating characteristic (ROC) curve obtained by the "rating" method, or by mathematical predictions based on patient characteristics, is presented. It is shown that in such a setting the area represents the probability that a randomly chosen diseased subject is (correctly) rated or ranked with greater suspicion than a randomly chosen non-diseased subject. Moreover, this probability of a correct ranking is the same quantity that is estimated by the already well-studied nonparametric Wilcoxon statistic. These two relationships are exploited to (a) provide rapid closed-form expressions for the approximate magnitude of the sampling variability, i.e., standard error that one uses to accompany the area under a smoothed ROC curve, (b) guide in determining the size of the sample required to provide a sufficiently reliable estimate of this area, and (c) determine how large sample sizes should be to ensure that one can statistically detect difference...
19,398 citations
Book•
01 Jan 1983
TL;DR: The methodology used to construct tree structured rules is the focus of a monograph as mentioned in this paper, covering the use of trees as a data analysis method, and in a more mathematical framework, proving some of their fundamental properties.
Abstract: The methodology used to construct tree structured rules is the focus of this monograph. Unlike many other statistical procedures, which moved from pencil and paper to calculators, this text's use of trees was unthinkable before computers. Both the practical and theoretical sides have been developed in the authors' study of tree methods. Classification and Regression Trees reflects these two sides, covering the use of trees as a data analysis method, and in a more mathematical framework, proving some of their fundamental properties.
14,825 citations
TL;DR: In this article, the authors discuss the problem of estimating the sampling distribution of a pre-specified random variable R(X, F) on the basis of the observed data x.
Abstract: We discuss the following problem given a random sample X = (X 1, X 2,…, X n) from an unknown probability distribution F, estimate the sampling distribution of some prespecified random variable R(X, F), on the basis of the observed data x. (Standard jackknife theory gives an approximate mean and variance in the case R(X, F) = \(\theta \left( {\hat F} \right) - \theta \left( F \right)\), θ some parameter of interest.) A general method, called the “bootstrap”, is introduced, and shown to work satisfactorily on a variety of estimation problems. The jackknife is shown to be a linear approximation method for the bootstrap. The exposition proceeds by a series of examples: variance of the sample median, error rates in a linear discriminant analysis, ratio estimation, estimating regression parameters, etc.
14,483 citations