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I am facing a problem with the classification of an imbalanced sample, and I was looking into solutions for both dealing with the imbalance (e.g. oversampling/undersampling) and a metric which would be suitable for the estimation of the classifier performance on the imbalanced sample.

I need to mention that my sample is not extremely imbalanced, at most 1:2 to 1:3 ratio.

Regarding the metrics, I found many alternatives to accuracy, except for the one which seemed very logical to me -- what I call in my head "normalized accuracy". Simply said, it is the average of the ratios of the correctly identified samples within each class. On a confusion matrix for two classes, it would be (TP/(TP+FN) + TN/(TN+FP))/2. This seems very logical to me, symmetrical and extendible to multilabel classification.

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However, when I tried to find any mentions in the literature regarding this, I completely and repeatedly failed. Is it known under another name? Is it somehow so flawed that nobody ever discusses it anymore? Can someone enlighten me about this?

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Your measure is a linear transform of Youden’s J statistic. See wikipedia Youden's J statistic page for more information about how is computed. J statistic has one advantage, it’s range which make it easier to compare.

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