Multi-label classification

In the multi-label problem there is no constraint on how many of the classes the instance can be assigned to. Formally, multi-label classification is the problem of finding a model that maps inputs x to binary vectors y (assigning a value of 0 or 1 for each element (label) in y).

Problem transformation methods

Transformation into binary classification problems
- binary relevance
  
  amounts to independently training one binary classifier for each label.
  
  Although this method of dividing the task into multiple binary tasks may resemble superficially the one-vs.-all (OvA) and one-vs.-rest (OvR) methods for multiclass classification, it is essentially different from both, because a single classifier under binary relevance deals with a single label, without any regard to other labels whatsoever.
- classifier chain
  
  It differs from binary relevance in that labels are predicted sequentially, and the output of all previous classifiers (i.e. positive or negative for a particular label) are input as features to subsequent classifiers.
Transformation into multi-class classification problem
- label powerset
Ensemble methods

A set of multi-class classifiers can be used to create a multi-label ensemble classifier. For a given example, each classifier outputs a single class (corresponding to a single label in the multi-label problem). These predictions are then combined by an ensemble method, usually a voting scheme where every class that receives a requisite percentage of votes from individual classifiers (often referred to as the discrimination threshold[8]) is predicted as a present label in the multi-label output.