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Hierarchical multi-label classification problems typically deal with datasets with many attributes and labels, which can negatively impact the classifier performance. The application of dimensionality reduction methods can significantly improve the performance of classifiers. Dimensionality reduction can be performed by feature extraction or feature selection, according to the problem domain and datasets characteristics. This work carried out a systematic literature mapping to identify the approaches and techniques of dimensionality reduction that have been used in hierarchical multi-label classification tasks. Searches were performed on 7 important databases for the Computer Science field. From a list of 184 retrieved papers, 12 were selected for analysis, from which it was possible to determine a general overview of studies conducted from 2010 to 2022. It was identified that feature selection was the most frequent reduction method, with filter approach standing out. In addition, it was detected that most of the works used tree hierarchical structure. As its main outcome, this paper presents the state of the art of dimensionality reduction problem for hierarchical multi-label classification, indicating trends and research issues in the field. [ABSTRACT FROM AUTHOR]