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      A Comparison of MCC and CEN Error Measures in Multi-Class Prediction

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      PLoS ONE
      Public Library of Science

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          Abstract

          We show that the Confusion Entropy, a measure of performance in multiclass problems has a strong (monotone) relation with the multiclass generalization of a classical metric, the Matthews Correlation Coefficient. Analytical results are provided for the limit cases of general no-information (n-face dice rolling) of the binary classification. Computational evidence supports the claim in the general case.

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          Most cited references4

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          The meaning and use of the area under a receiver operating characteristic (ROC) curve.

          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 differences in the accuracy of diagnostic techniques.
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            Comparing two K-category assignments by a K-category correlation coefficient.

            J Gorodkin (2004)
            Predicted assignments of biological sequences are often evaluated by Matthews correlation coefficient. However, Matthews correlation coefficient applies only to cases where the assignments belong to two categories, and cases with more than two categories are often artificially forced into two categories by considering what belongs and what does not belong to one of the categories, leading to the loss of information. Here, an extended correlation coefficient that applies to K-categories is proposed, and this measure is shown to be highly applicable for evaluating prediction of RNA secondary structure in cases where some predicted pairs go into the category "unknown" due to lack of reliability in predicted pairs or unpaired residues. Hence, predicting base pairs of RNA secondary structure can be a three-category problem. The measure is further shown to be well in agreement with existing performance measures used for ranking protein secondary structure predictions. Server and software is available at http://rk.kvl.dk/.
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              Evaluating diagnostic tests: The area under the ROC curve and the balance of errors.

              David Hand (2010)
              Because accurate diagnosis lies at the heart of medicine, it is important to be able to evaluate the effectiveness of diagnostic tests. A variety of accuracy measures are used. One particularly widely used measure is the AUC, the area under the receiver operating characteristic (ROC) curve. This measure has a well-understood weakness when comparing ROC curves which cross. However, it also has the more fundamental weakness of failing to balance different kinds of misdiagnoses effectively. This is not merely an aspect of the inevitable arbitrariness in choosing a performance measure, but is a core property of the way the AUC is defined. This property is explored, and an alternative, the H measure, is described. (c) 2010 John Wiley & Sons, Ltd.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS One
                PLoS ONE
                plos
                plosone
                PLoS ONE
                Public Library of Science (San Francisco, USA )
                1932-6203
                2012
                8 August 2012
                : 7
                : 8
                : e41882
                Affiliations
                [1]Fondazione Bruno Kessler, Trento, Italy
                Sapienza University of Rome, Italy
                Author notes

                Competing Interests: The authors have declared that no competing interests exist.

                Conceived and designed the experiments: GJ SR. Performed the experiments: GJ SR. Analyzed the data: GJ SR. Contributed reagents/materials/analysis tools: GJ SR. Wrote the paper: GJ CF SR.

                Article
                PONE-D-12-03597
                10.1371/journal.pone.0041882
                3414515
                22905111
                438a1721-7316-4f00-b139-f853a887e066
                Copyright @ 2012

                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.

                History
                : 31 January 2012
                : 27 June 2012
                Page count
                Pages: 8
                Funding
                The authors acknowledge funding by the European Union FP7 Project HiperDART and by the PAT funded Project ENVIROCHANGE. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
                Categories
                Research Article
                Biology
                Computational Biology
                Computer Science
                Algorithms
                Computer Applications
                Mathematics
                Mathematical Computing
                Probability Theory
                Statistical Distributions
                Statistical Medians
                Statistics
                Biostatistics
                Confidence Intervals
                Contingency Tables
                Statistical Methods

                Uncategorized
                Uncategorized

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