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Table 6 Performance measure definitions for multi-class classification. The performance measures accuracy, precision, recall, correlation coefficient, and kappa coefficient are used to evaluate the performance of our machine learning approaches [45]. Accuracy is the fraction of overall predictions that are correct. Precision is the ratio of predicted true positive examples to the total number of actual positive examples. Recall is the ratio of predicted true positives to the total number of examples predicted as positive. Correlation coefficient measures the correlation between predictions and actual class labels. Kappa coefficient is used as a measure of agreement between two random variables (predictions and actual class labels). The table displays the general definition of each measure, where M = the total number of classes and N = the total number of examples, x ik represents the number of examples in row i and column k of the given confusion matrix.

From: Exploring inconsistencies in genome-wide protein function annotations: a machine learning approach

Performance Measure

Definition

Accuracy (class i)

∑ i = 1 M x i i N MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWcaaqaamaaqadabaGaemiEaG3aaSbaaSqaaiabdMgaPjabdMgaPbqabaaabaGaemyAaKMaeyypa0JaeGymaedabaGaemyta0eaniabggHiLdaakeaacqWGobGtaaaaaa@38B1@

Precision (class i)

x i i ∑ k = 1 M x k i MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWcaaqaaiabdIha4naaBaaaleaacqWGPbqAcqWGPbqAaeqaaaGcbaWaaabmaeaacqWG4baEdaWgaaWcbaGaem4AaSMaemyAaKgabeaaaeaacqWGRbWAcqGH9aqpcqaIXaqmaeaacqWGnbqta0GaeyyeIuoaaaaaaa@3BEF@

Recall (class i)

x i i ∑ k = 1 M x i k MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWcaaqaaiabdIha4naaBaaaleaacqWGPbqAcqWGPbqAaeqaaaGcbaWaaabmaeaacqWG4baEdaWgaaWcbaGaemyAaKMaem4AaSgabeaaaeaacqWGRbWAcqGH9aqpcqaIXaqmaeaacqWGnbqta0GaeyyeIuoaaaaaaa@3BEF@

Correlation Coefficient (class i)

( x i i * ∑ h ≠ i x h h ) − ( ∑ k = 1 M x k i * ∑ j = 1 M x i j ) ( x i i + ∑ k = 1 M x k i ) ( x i i + ∑ j = 1 M x i j ) ( ∑ h ≠ i x h h + ∑ k = 1 M x k i ) ( ∑ h ≠ i x h h + ∑ j = 1 M x i j ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@AB9F@

Kappa Coefficient

∑ i = 1 M x i i − ∑ h = 1 M ( ∑ k = 1 M x k h * ∑ j = 1 M x h j ) N − ∑ h = 1 M ( ∑ k = 1 M x k h * ∑ j = 1 M x h j ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@7820@