# Should I use multi-label classification?

I have a classification problem with 2 classes (positive and negative). Usually, in such classification problems, all the samples will be labelled either 'positive' or 'negative'. In my dataset, some of the samples possess a combination of both positive and negative characteristics. Formally, if the dataset is $x$, then,

$x=x_1 \cup x_2 \cup x_3$

where $x_1$ is the set of all positive samples, $x_2$ is the set of all negative samples and $x_3$ is the set of samples that contain the characteristics of both the classes. As far as I could think of, this situation could be handled in 2 ways,

1. Ignore $x_3$ (samples that contain characteristics of both classes) and treat the problem as a traditional binary classification.
2. Label the samples in $x_3$ with both labels (positive & negative) and consider this as a multi-label classification problem.

I wish to follow the second option, as it is more natural choice. The reason being, ignoring some samples from the dataset gives me a feeling of manipulating the dataset artificially which may affect the performance of the classifier in the real world scenario. In this context, I have the following questions,

1. Is it correct to treat this a multi-label classification problem. If so, is the intuition which is explained in the previous paragraph correct?
2. Is there any other learning paradigm that can handle this scenario? If so, please provide reference to relevant literature.
• Please, clarify for me. Is X1 a group of training examples with positive labels, and X2 a group with negative labels, and X3 a group with mixed labels? Is to, can you verify that they all have the same features (variables)? If this is correct, why have you divided them into groups? If you could give an example of the input (features) and output (labels), it might be clearer. – John Yetter May 18 '14 at 16:49
• $x$ is the set of training examples. I meant to say $x$ is made up of 3 types of samples i.e. positive, negative and mixed. //can you verify that they all have the same features (variables)?// - Yes, they do – Annamalai N May 18 '14 at 16:52