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Positive and Negative Predictive Values

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  • True Positives: The number of points that the classifier correctly predicts as positive.

    $$TP=n_{11}=|{x_i|\hat{y_i}=y_i=c_1}|$$

  • False Positives: The number of points the classifier predicts to be positive, which in fact belong to the negative class.

    $$FP=n_{21}=|{x_i|\hat{y_i}=c_1 \land y_i=c_2}|$$

  • False Negatives: The number of points the classifier predicts to be in the negative, which in fact belong to the positive class.

    $$FN=n_{12}=|{x_i|\hat{y_i}=c_2 \land y_i=c_1}|$$

  • True Negatives: The number of points that the classifier correctly predicts as negative.

    $$TN=n_{22}=|{x_i|\hat{y_i}=y_i=c_2}|$$

True 是预测正确的,False 是预测错误的,True 和 False 后面是预测的结果。

  • Error Rate

    $$Error\ Rate=\frac{FP+FN}{n}=1-Accuracy$$

推广到多分类

对于每个分类,可以将当前分类作为 Positive,所有其它分类作为 Negative。TP 为正确归类到当前分类,TN 为正确归类到其它分类,FP 为错误归类到当前分类,FN 为错误归类到其它分类。

Footnotes

  1. Positive and negative predictive values - Wikipedia