About the average option in sklearn.metrics.f1_score

What is f1 score?

It is an index of the balance between Recall (recall rate, sensitivity) and Precision (goodness of fit, accuracy) indicated by. Since it is a harmonic mean, the score will be low if either one is extremely low.

Multi-class classification

For the sake of simplicity, classify into 3 classes (4 or more classes can be considered in the same way)

When there is a confusion matrix like this, TP, FP, and FN are defined as follows.

FP is the sum of vertical elements and FN is the sum of horizontal elements other than diagonal elements.

sklearn.metrics.f1_score [https://scikit-learn.org/stable/modules/generated/sklearn.metrics.f1_score.html] If you look at (), you can see the options " binary ", " micro ", " macro ", There are " weighted ", " samples ". (Same for recall_score and precision_score) " binary " is used in binary classification. Others are described below.

"micro"

1. Calculate TP, FP, FN as a whole.

   TP	FP	FN
   45	22	22

2. Calculate with the obtained TP, FP.FN $f1 = \frac{2 \times TP}{2 \times TP + FP + FN} = \frac{90}{90+22+22} = 0.67164179104\dots$

"macro"

1. Calculate Recall and Precision for each class

   class	Recall	Precision
   a	\frac{10}{18}	\frac{10}{18}
   b	\frac{20}{27}	\frac{20}{26}
   c	\frac{15}{22}	\frac{15}{23}

2. Calculate the average Recall and Precision

   Recall	Precision
   \frac{1}{3}\sum{Recall}	\frac{1}{3}\sum{Precision}

3. Calculate f1 with the calculated average

   \frac{1}{\frac{1}{\frac{1}{3}\sum{Recall}} \times \frac{1}{\frac{1}{3}\sum{Precision}}}

"weighted"

1. Multiply the number of data in each class by the individual Recall, Precision

   class	Recall	Precision
   a	\frac{10}{18} \times 18	\frac{10}{18}\times 18
   b	\frac{20}{27}\times 18	\frac{20}{26}\times 18
   c	\frac{15}{22}\times 18	\frac{15}{23}\times 18

2. Divide the sum of Recall and Precision by the total number of data

   Recall	Precision
   \frac{1}{67}\sum{Recall}	\frac{1}{67}\sum{Precision}

3. Calculate f1 with the calculated average

   \frac{1}{\frac{1}{\frac{1}{67}\sum{Recall}} \times \frac{1}{\frac{1}{67}\sum{Precision}}}

"samples" I'm not sure, so I'll add it as soon as I understand it.