Research on Machine learning (ML) explainability has received a lot of focus in recent times. The interest, however, mostly focused on supervised models, while other ML fields have not had the same level of attention. Despite its usefulness in a variety of different fields, unsupervised learning explainability is still an open issue. In this paper, we present a Visual Analytics framework based on eXplainable AI (XAI) methods to support the interpretation of Dimensionality reduction methods. The framework provides the user with an interactive and iterative process to investigate and explain user-perceived patterns for a variety of DR methods by using XAI methods to explain a supervised method trained on the selected data. To evaluate the effectiveness of the proposed solution, we focus on two main aspects: the quality of the visualization and the quality of the explanation. This challenge is tackled using both quantitative and qualitative methods, and due to the lack of pre-existing test data, a new benchmark has been created. The quality of the visualization is established using a well-known survey-based methodology, while the quality of the explanation is evaluated using both case studies and a controlled experiment, where the generated explanation accuracy is evaluated on the proposed benchmark. The results show a strong capacity of our framework to generate accurate explanations, with an accuracy of 89% over the controlled experiment. The explanation generated for the two case studies yielded very similar results when compared with pre-existing, well-known literature on ground truths. Finally, the user experiment generated high quality overall scores for all assessed aspects of the visualization.