# Multilabel Text Classification with Label-Dependent Representation
## 3 Label-Dependent Representation  
Although in recent years there has been a growth in the interest of the scientific community in deep learning models, there is a debate between the \"white box\" vs. \"black box\" approaches, with advantages and disadvantages of both approaches. Superficial learning highlights the feasibility of working with relatively small data sets and interpretability. Deep learning models stand out for their good performance and robustness. Therefore, it is not possible to completely rule out techniques and models based on shallow learning, especially when the set of training cases does not have a large volume of data and the set of features is not very extensive.  
As already mentioned, in this approach, it is planned to use classification methods based on shallow learning combining representation modification with problem transformation. Although this research does not use classification methods based on deep learning, such as BERT and its variants, it would also be possible to use this approach to modify the characteristics of the representation of the original texts and generate to new layers or inputs to deep learning methods, especially when working with small data sets. This would also give better interpretability to the deep learning models.  
On the other hand, in the case of the problem of multilabeled texts, the classification models must deal with data sets with a high cardinality, density, and diversity of labels. Cardinality measures the average number of labels associated with each document, density is the cardinality divided by the number of labels, and diversity represents the percentage of label sets present in the corpus divided by the number of possible label sets. In this work, we use data sets with a cardinality of between 1.18 and 3.28, a density of between 0.014 and 0.098, and a diversity of between 0.041 and 0.442.  
In this section, the well-known _tf-idf_[39] representation is explained, and our proposed function for the weighting of _rfl_ terms is presented. Based on the latter, we propose two new representations, one based on the Multivariate Bernoulli model called _bin-rfl_, and another based on the Multinomial _tf-rfl_ model. In this type of representation, the indicator \(f_{t,d}\) can have values of between zero and one ([0, 1]), is called the Multinomial Model by [36], and is different from the Bernoulli Multivariate Model, where the indicator is \(bin_{t,d}\), which is represented by one when the term \(t\) exists at least once in the document \(d\); that is, it can have a value of zero or one ([0, 1]). The factor based on the Bernoulli Multivariate Model is called a Binary Representation or Boolean Model. Many problems, either by their nature or by the measurements that can be obtained from them, use the representation model based on the Multivariate Bernoulli Model.  
This raises the hypothesis that a supervised modification to the text representation that considers frequency representations or binary representations, together with a function for the supervised weighting of the terms that is based on the known examples, according to their labels, could improve the performances of the classifiers significantly. When referring to supervised modification, what we are proposing is a modification of the representation based on the analysis of the labeled examples of the training set, which is why it is supervised. For the term weighting method for multilabel problems, we will use as variables those described in Table 4: \(a_{t,\lambda_{j}}\), which represents the number of documents in the category \(\lambda_{j}\) containing the term \(t\) and \(d_{t,\lambda_{j}}\) representing the number of documents in the category \(\lambda_{j}\) that do not contain the term \(t\).