Accuracy, Precision, Recall, F1

Accuracy, precision, recall, and f1 are 4 common metrics in classification evaluation.

• True Negative (TN): case was negative and predicted negative
• True Positive (TP): case was positive and predicted positive
• False Negative (FN): case was positive but predicted negative
• False Positive (FP): case was negative but predicted positive

	Predicted Negative	Predicted Positive
Negative Cases	TN	FP
Positive Cases	FN	TP

Accuracy

The percentage of successful prediction

$$\frac{TN + TP}{TN + FN + TP + FP}$$

Precision

How many seleted items are relevant

$$\frac{TP}{TP + FP}$$

Recall

How many relevant items are selected

$$\frac{TP}{TP + FN}$$

Harmonic score

Sometimes precision and recall is contradictory. For example, if we only found 1 case which is correctly predicted, the precision is 100% while the recall is probably running extremely low.

Therefore, we might use Harmonic score, for merging multiple measures.

$$f(x_1...x_n) = \frac{n}{\frac1{x_1} + ... + \frac1{x_n}}$$

F1 score

$$f(x, y) = \frac2{\frac1{x} + \frac1{y}}$$ is called harmonic sum.$$

F_1 = \frac2{\frac1{recall} + \frac1{precision}} = 2 * \frac{precision ∗ recall}{precision + recall}

$symmetric, x,y are same important.$f\in(0, 1]$when$x, y\in [0, 1]$$. Either x or y increase, f increase.

Reference

How Are Precision and Recall Calculated?. Retrieved from https://www.kdnuggets.com/faq/precision-recall.html