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# F-1 Score for Multi-Class Classification

Last modified: November 15, 2022

**1. Introduction**

**In this tutorial, we’ll talk about how to calculate the F-1 score in a multi-class classification problem.** Unlike binary classification, multi-class classification generates an F-1 score for each class separately.

We’ll also explain how to compute an averaged F-1 score per classifier in Python, in case a single score is desired.

**2. F-1 Score**

**F-1 score is one of the common measures to rate how successful a classifier is.** It’s the harmonic mean of two other metrics, namely: precision and recall. In a binary classification problem, the formula is:

The F-1 Score metric is preferable when:

- We have imbalanced class distribution
- We’re looking for a balanced measure between precision and recall (Type I and Type II errors)

**As the F-1 score is more sensitive to data distribution, it’s a suitable measure for classification problems on imbalanced datasets.**

**3. Multi-Class F-1 Score Calculation**

**For a multi-class classification problem, we don’t calculate an overall F-1 score. Instead, we calculate the F-1 score per class in a one-vs-rest manner.** In this approach, we rate each class’s success separately, as if there are distinct classifiers for each class.

As an illustration, let’s consider the confusion matrix below with a total of 127 samples:

Now let’s calculate the F-1 score for the first class, which is *class a*. We first need to calculate the precision and recall values:

Then, we apply the formula for *class a*:

Similarly, we first calculate the precision and recall values for the other classes:

The calculations then lead to per-class F-1 scores for each class:

**4. Implementation**

**In the Python sci-kit learn library, we can use the F-1 score function to calculate the per class scores of a multi-class classification problem. **

**We need to set the average parameter to None to output the per class scores.**

For instance, let’s assume we have a series of real y values (*y_true*) and predicted y values (*y_pred*). Then, let’s output the per class F-1 score:

```
from sklearn.metrics import f1_score
f1_score(y_true, y_pred, average=None)
```

In our case, the computed output is:

`array([0.62111801, 0.33333333, 0.26666667, 0.13333333])`

**On the other hand, if we want to assess a single F-1 score for easier comparison, we can use the other averaging methods.** To do so, we set the *average* parameter.

Here we’ll examine three common averaging methods.

The first method, *micro* calculates positive and negative values globally:

`f1_score(y_true, y_pred, average='micro')`

In our example, we get the output:

`0.49606299212598426`

Another averaging method, *macro*, take the average of each class’s F-1 score:

`f1_score(y_true, y_pred, average='macro')`

gives the output:

`0.33861283643892337`

Note that the macro method treats all classes as equal, independent of the sample sizes.

As expected, the micro average is higher than the macro average since the F-1 score of the majority class (*class a*) is the highest.

The third parameter we’ll consider in this tutorial is *weighted*. The class F-1 scores are averaged by using the number of instances in a class as weights:

`f1_score(y_true, y_pred, average='weighted')`

generates the output:

`0.5728142677817446`

In our case, the weighted average gives the highest F-1 score.

**We need to select whether to use averaging or not based on the problem at hand.**

**5. Conclusion**

In this tutorial, we’ve covered how to calculate the F-1 score in a multi-class classification problem.

Firstly, we described the one-vs-rest approach to calculate per class F-1 scores.

Also, we’ve covered three ways of calculating a single average score in Python.