Summary of the datasets.

Clustering is an unsupervised machine learning technique whose goal is to cluster unlabeled data. But traditional clustering methods only output a set of results and do not provide any explanations of the results. Although in the literature a number of methods based on decision tree have been proposed to explain the clustering results, most of them have some disadvantages, such as too many branches and too deep leaves, which lead to complex explanations and make it difficult for users to understand. In this paper, a hypercube overlay model based on multi-objective optimization is proposed to achieve succinct explanations of clustering results. The model designs two objective functions based on the number of hypercubes and the compactness of instances and then uses multi-objective optimization to find a set of nondominated solutions. Finally, an Utopia point is defined to determine the most suitable solution, in which each cluster can be covered by as few hypercubes as possible. Based on these hypercubes, an explanations of each cluster is provided. Upon verification on synthetic and real datasets respectively, it shows that the model can provide a concise and understandable explanations to users.