## 2 Preliminaries
### Prototype Selection and Label-Specific Feature Learning  
Nowadays, one of the main challenges for supervised learning algorithms is still how to deal with raw datasets. Data pre-processing is an often unattended but important step in the data mining process [22]. Data gathering is often a poorly monitored process, resulting in low-quality datasets. If there is a lot of irrelevant and redundant information or noisy and unreliable data, then knowledge discovery is more difficult to carry out. Data reduction techniques [22] allow us to obtain a reduced representation of the original data but maintaining the essential structure and integrity. Such pre-processing techniques usually lead to improved performance of subsequent learners. A frequent problem with real datasets is their big volume, as well as the presence of noise and anomalies that complicate the learning process. Instance selection is to choose a subset of data to achieve the original purpose of a data mining application as if the whole data is used [23]. The optimal outcome of instance selection is a stand-alone model, with a minimal data sample that can perform tasks with little or no performance degradation. Instance selection has been successfully applied to various problem types like imbalanced learning [44], data streams [45], regression [46], subgroup discover in large size datasets [47]. The research conducted in [48] is also of interest to investigate the impact of instance selection on the underlying structure of a dataset by analyzing the distribution of sample types. However, as of today, instance selection has not been extensively researched in the domain of MLL and to date only few methods have been made available [26; 27; 28]. As for LDL, we have not been able to find any studies to date. Prototype Selection [22] methods are Instance Selection methods that expect to find training sets that offer the best ranking accuracy and reduction rates by using instances-based classifiers which consider a certain similarity or distance measure. A widely used categorization of prototype selection methods consists of three types of techniques [24]: Condensation, where the aim is to retain border points, preserving the accuracy of the training system; Edition, where the objective is to eliminate boundary points that are considered noise or do not match their neighbors but without removing the internal points of each dataset; or Hybrid methods that try to find a small set of training data while maintaining the performance of the classifier. The best approach considering the trade-off between reduction and accuracy is usually the hybrid technique. To name just a few successful cases when applying prototype selection, [49] proposes a prototype selection algorithm called MONIPS that has proved to be competitive with classical prototype selection solutions adapted to monotonic classification. The experimental study presented in [50] shows a significant improvement when prototype selection is applied to dynamic classifier and ensemble selection. Another widely used pre-processing technique is the reduction of the data dimensionality by means of feature selection [25]. The main idea is to replace the original set of features by a new subset that extract the main information and provide an accurate classification. However, in MLL and LDL, the strategy of selecting a set of characteristics shared by all labels may not be optimal since each label may be described by a specific subset of characteristics of their own. Label-specific feature learning has been widely studied in MLL. For instance, LIFT [29] firstly builds specific features of each label by performing cluster analysis on its positive and negative instances, and then conducts training and testing by querying the cluster results. LLSF [30] proposes learning label-specific features for each class label by considering pairwise (i.e., second-order) label correlations.