Precision & Recall in
Multiclass
Classification
Prof. Dr. Mirco Schoenfeld
multiclass?
But how is it in multiclass classification?
We usually do not have any notions of positive or negative.
multiclass, not multilabel
We only consider multiclass, not multilabel
classification.
Accuracy
For accuracy, this is easy:
\(\text{Accuracy} = \frac{\text{Correct
predictions}}{\text{All predictions}}\)
Downsides of accuracy
As always, accuracy is not the perfect measurement.
It disregards class balance and the cost of different
errors.
Precision and Recall in Multiclass classification
To consider precision and recall in multiclass
classification,
obtain these metrics for each class
individually.
Precision and Recall in Multiclass classification
For Class A, this becomes:
\(\text{Precision}_{\text{Class A}} =
\frac{\text{TP}_{\text{Class A}}}{\text{TP}_{\text{Class A}} +
\text{FP}_{\text{Class A}}}\)
\(\text{Recall}_{\text{Class A}} =
\frac{\text{TP}_{\text{Class A}}}{\text{TP}_{\text{Class A}} +
\text{FN}_{\text{Class A}}}\)
Overall Precision and Recall in Multiclass classification
In the end, obtain an average of
precision and recall of
individual classes.
Either the macro-average, or the micro-average.
Macro Average
The Macro Average:
\(\text{Precision} =
\frac{\text{Precision}_{\text{Class A}} + \dots{} +
\text{Precision}_{\text{Class N}}}{N}\)
\(\text{Recall} =
\frac{\text{Recall}_{\text{Class A}} + \dots{} +
\text{Recall}_{\text{Class N}}}{N}\)
Micro Average
The Micro Average:
\(\text{Precision} =
\frac{\text{TP}_{\text{Class A}} + \dots{} + \text{TP}_{\text{Class
N}}}{\text{TP}_{\text{Class A}} + \text{FP}_{\text{Class A}} + \dots{} +
\text{TP}_{\text{Class N}} + \text{FP}_{\text{Class N}}}\)
\(\text{Recall} =
\frac{\text{TP}_{\text{Class A}} + \dots{} + \text{TP}_{\text{Class
N}}}{\text{TP}_{\text{Class A}} + \text{FN}_{\text{Class A}} + \dots{} +
\text{TP}_{\text{Class N}} + \text{FN}_{\text{Class N}}}\)
Macro vs micro
Macro-averaging gives equal weight to each class
Micro-averaging gives equal weight to each instance
