## 1 Introduction  
A supervised learning process is the machine learning task of training a function that maps an input to an output based on data points with known outputs. Classification is the process of predicting to which of a set of categories a new observation belongs. Thus, the purpose of classification is to achieve a model that will be able to classify the right class to an unknown pattern. However, there are an increasing number of problems where a pattern can have several labels simultaneously associated. Examples can be found in genetics [1], image classification [2], etc. The generalization of the classic classification is Multi-Label Learning (MLL) [3; 4; 5; 6], where multiple labels can be assigned to each instance. Nevertheless, in many real-world problems we may face cases where MLL is still not enough, as the degree of description of each label is different. To appoint only one dataset used in this paper, the biological experiments on yeast genes [7] during a period of time yield different levels of gene expression in a time serie. The exact level of expression at any point in time is of less importance. What becomes really decisive is the overall expression distribution over the whole period of time. If the learning goal is to predict that distribution for a particular gene, it cannot easily fit into the MLL framework because the role of each output in the distribution is critical, and there is no division of relevant and irrelevant labels at all. The proposal of Label Distribution Learning (LDL) appeared for first time in 2013 [8] and was formally introduced in 2016 [9] in order to handle ambiguity on the label side of the mapping when one instance is not mandatorily matched to one single label. The main objective of this paradigm is to respond to the question \"how much does each label describe the instance?\" instead of \"which label can describe the instance?\". Numerous studies have been conducted by applying the LDL framework to diverse real-life problem solving scenarios, e.g., facial age estimation [8], pre-release prediction of crowd opinion on movies [10], crowd counting in public video surveillance [11], sense beauty recognition [12], image emotion classification [13], personality recognition on social media [14], head pose estimation [15], etc. Further research has focused more on the development of new learners or on the adaptation of existing ones such as: instance-based algorithms (e.g., AA-\(k\)NN [9]), optimization algorithms (e.g., SA-IIS, SA-BFGS [9] or LDL-SCL [16]), decision trees (e.g., LDL forests [17]), deep learning algorithms (e.g., Deep Label Distribution [18]), or ensembles strategies (e.g., Logistic boosting regression for LDL [19], Structured random forest for LDL [20]). AA-\(k\)NN [9] has proven to be a very competitive algorithm in previous experimental studies, achieving acceptable results and allowing an explainable model [21]. However, like any other instance-based algorithm, it suffers from several handicaps: it needs large memory requirements to store the training set, it is not efficient predicting due to the multiple computations of similarities between the test and training samples and it presents a low tolerance to noise because it uses all the data as relevant. Nowadays, one of the main challenges of supervised learning algorithms is still how to deal with raw datasets. Data collection is usually an unsupervised process, leading to datasets with redundant information, noisy data or irrelevant features. Hence, data pre-processing is an important step in the data mining process, that can mitigate this type of problem and generate improved datasets. The purpose of this paper is to address the LDL problem from the data pre-processing stage, by applying data reduction techniques which will allow us to have a reduced representation of the original data while maintaining the essential structure and integrity [22]. These pre-processing techniques often result in better performance of subsequent learners.