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In machine learning, **multi-label classification** and the strongly related problem of **multi-output classification** are variants of the classification problem where multiple target labels must be assigned to each instance. Multi-label classification should not be confused with multiclass classification, which is the problem of categorizing instances into more than two classes. Formally, multi-label learning can be phrased as the problem of finding a model that maps inputs **x** to vectors **y**, rather than scalar outputs as in the ordinary classification problem.

There are two main methods for tackling the multi-label classification problem:^{[1]} problem transformation methods and algorithm adaptation methods. Problem transformation methods transform the multi-label problem into a set of binary classification problems. Algorithm adaptation methods adapt the algorithms to directly perform multi-label classification.

## Problem transformation[edit | edit source]

Several problem transformation methods exist for multi-label classification; the baseline approach^{[2]}
amounts to training one classifier per label, similar to the one-vs.-all (OvA, also one-vs.-rest, OvR) method for multiclass classification. Given an unseen sample, the combined model then predicts all labels for this sample for which the respective binary classifiers predict a positive result.
(This method has also been called the "binary relevance" method.^{[3]})

Various other transformations exist: the label combinations (LC) transformation, creates one binary classifier for every possible label combination. Other transformation methods include RAkEL^{[4]} and classifier chains.^{[3]} Various problem transformation methods have been developed such as Ml-kNN,^{[5]} a variant of the k-nearest neighbors lazy classifiers. A more detailed description of the most well known methods for multi-label classification and an extensive empirical evaluation can be found here.^{[6]}

## Evaluation[edit | edit source]

Evaluation metrics for multi-label classification are inherently different from those used in multi-class (or binary) classification, due to the inherent differences of the classification problem. The following metrics are typically used:

- Hamming loss: the percentage of the wrong labels to the total number of labels. This is a loss function, so the optimal value is zero.
- Label-based accuracy
- Exact match: is the most strict metric, indicating the percentage of samples that have all their labels classified correctly.

## Implementations and datasets[edit | edit source]

Java implementations of multi-label algorithms are available in the Mulan and Meka software packages, both based on Weka.

The scikit-learn python package implements some multi-labels algorithms and metrics.

A list of commonly used multi-label data-sets is available at the Mulan website.

## References[edit | edit source]

- ↑ Grigorios Tsoumakas, Ioannis Katakis.
*Multi-Label Classification: An Overview*. International Journal of Data Warehousing & Mining, 3(3), 1-13, July–September 2007. - ↑ (2012) "The landmark selection method for multiple output prediction" in
*ICML*.*{{{booktitle}}}*. - ↑
^{3.0}^{3.1}Jesse Read, Bernhard Pfahringer, Geoff Holmes, Eibe Frank. Classifier Chains for Multi-label Classification. Machine Learning Journal. Springer. Vol. 85(3), (2011). - ↑ Konstantinos Trohidis, Grigorios Tsoumakas, George Kalliris, Ioannis Vlahavas Multi-label Classification of Music into emotions ISMIR 2008
- ↑ Zhang, M.L. and Zhou, Z.H. ML-KNN: A lazy learning approach to multi-label learning
- ↑ Gjorgji Madjarov, Dragi Kocev, Dejan Gjorgjevikj, Sašo Džeroski. An extensive experimental comparison of methods for multi-label learning. Pattern Recognition. Vol. 45(9), (2012).