Precision/recall for multiclass-multilabel classification

machine-learning classification multilabel-classification precision-recall
MaVe picture MaVe · Jan 25, 2012 · Viewed 27.4k times · Source

I'm wondering how to calculate precision and recall measures for multiclass multilabel classification, i.e. classification where there are more than two labels, and where each instance can have multiple labels?

Answer

phoxis picture phoxis · Sep 9, 2016

For multi-label classification you have two ways to go First consider the following.

  • $n$ is the number of examples.
  • $Y_i$ is the ground truth label assignment of the $i^{th}$ example..
  • $x_i$ is the $i^{th}$ example.
  • $h(x_i)$ is the predicted labels for the $i^{th}$ example.

Example based

The metrics are computed in a per datapoint manner. For each predicted label its only its score is computed, and then these scores are aggregated over all the datapoints.

  • Precision = $\frac{1}{n}\sum_{i=1}^{n}\frac{|Y_{i}\cap h(x_{i})|}{|h(x_{i})|}$ , The ratio of how much of the predicted is correct. The numerator finds how many labels in the predicted vector has common with the ground truth, and the ratio computes, how many of the predicted true labels are actually in the ground truth.
  • Recall = $\frac{1}{n}\sum_{i=1}^{n}\frac{|Y_{i}\cap h(x_{i})|}{|Y_{i}|}$ , The ratio of how many of the actual labels were predicted. The numerator finds how many labels in the predicted vector has common with the ground truth (as above), then finds the ratio to the number of actual labels, therefore getting what fraction of the actual labels were predicted.

There are other metrics as well.

Label based

Here the things are done labels-wise. For each label the metrics (eg. precision, recall) are computed and then these label-wise metrics are aggregated. Hence, in this case you end up computing the precision/recall for each label over the entire dataset, as you do for a binary classification (as each label has a binary assignment), then aggregate it.

The easy way is to present the general form.

This is just an extension of the standard multi-class equivalent.

  • Macro averaged $\frac{1}{q}\sum_{j=1}^{q}B(TP_{j},FP_{j},TN_{j},FN_{j})$

  • Micro averaged $B(\sum_{j=1}^{q}TP_{j},\sum_{j=1}^{q}FP_{j},\sum_{j=1}^{q}TN_{j},\sum_{j=1}^{q}FN_{j})$

Here the $TP_{j},FP_{j},TN_{j},FN_{j}$ are the true positive, false positive, true negative and false negative counts respectively for only the $j^{th}$ label.

Here $B$ stands for any of the confusion-matrix based metric. In your case you would plug in the standard precision and recall formulas. For macro average you pass in the per label count and then sum, for micro average you average the counts first, then apply your metric function.

You might be interested to have a look into the code for the mult-label metrics here , which a part of the package mldr in R. Also you might be interested to look into the Java multi-label library MULAN.

This is a nice paper to get into the different metrics: A Review on Multi-Label Learning Algorithms

Related questions

A simple explanation of Naive Bayes Classification

I am finding it hard to understand the process of Naive Bayes, and I was wondering if someone could explain it with a simple step by step process in English. I understand it takes comparisons by times occurred as a …

Read More
Difference between classification and clustering in data mining?

Can someone explain what the difference is between classification and clustering in data mining? If you can, please give examples of both to understand the main idea.

Read More
What are advantages of Artificial Neural Networks over Support Vector Machines?

ANN (Artificial Neural Networks) and SVM (Support Vector Machines) are two popular strategies for supervised machine learning and classification. It's not often clear which method is better for a particular project, and I'm certain the answer is always "it depends." …

Read More