Optimizing different loss functions in multilabel classifications

Multilabel classification (ML) aims to assign a set of labels to an instance. This generalization of multiclass classification yields to the redefinition of loss functions and the learning tasks become harder. The objective of this paper is to gain insights into the relations of optimization aims and some of the most popular performance measures: subset (or 0/1), Hamming, and the example-based F-measure. To make a fair comparison, we implemented three ML learners for optimizing explicitly each one of these measures in a common framework. This can be done considering a subset of labels as a structured output. Then, we use structured output support vector machines tailored to optimize a given loss function. The paper includes an exhaustive experimental comparison. The conclusion is that in most cases, the optimization of the Hamming loss produces the best or competitive scores. This is a practical result since the Hamming loss can be minimized using a bunch of binary classifiers, one for each label separately, and therefore, it is a scalable and fast method to learn ML tasks. Additionally, we observe that in noise-free learning tasks optimizing the subset loss is the best option, but the differences are very small. We have also noticed that the biggest room for improvement can be found when the goal is to optimize an F-measure in noisy learning tasks.