Data analysis plays an indispensable role in understanding different phenomena. One of the vital means of handling these data is to group them into a set of clusters given a measure of similarity. Usually, clustering methods deal with objects described by single-valued variables. Nevertheless, this representation is too restrictive for representing complex data, such as lists, histograms, or even intervals. Furthermore, in some problems, many dimensions are irrelevant and can mask existing clusters. In this regard, new interval-valued data clustering methods with regularizations and adaptive distances are proposed. These approaches consider that the boundaries of the interval-valued variables have the same and different importance for the clustering process. The algorithms optimize an objective function alternating three steps for obtaining the representatives of each group, a fuzzy partition, and the relevance weights of the variables. Experiments on synthetic and real data sets corroborate the robustness and usefulness of the proposed methods.

数据分析在理解不同现象方面起着不可或缺的作用。处理这些数据的一个重要方法是在给定相似性度量的情况下将它们分组到一组集群中。通常，聚类方法处理由单值变量描述的对象。然而，这种表示对于表示复杂数据（例如列表、直方图或什至间隔）来说过于严格。此外，在某些问题中，许多维度是不相关的，可以掩盖现有的集群。在这方面，提出了具有正则化和自适应距离的新的区间值数据聚类方法。这些方法认为区间值变量的边界对聚类过程具有相同和不同的重要性。该算法通过交替三个步骤优化目标函数，以获得每个组的代表、模糊分区和变量的相关权重。在合成和真实数据集上的实验证实了所提出方法的稳健性和实用性。