Dynamic clustering defines partitions within data and prototypes to each partition. Distance metrics are responsible for checking the closeness between instances and prototypes. Considering the literature about interval data, distances depend on interval bounds and the information inside the intervals is ignored. This paper proposes new distances, which explore the information inside of intervals. It also presents a mapping of intervals to points, which preserves their spatial location and internal variation. We formulate a new hybrid distance for interval data based on the well-known \(L_q\) distance for point data. This new distance allows for a weighted formulation of the hybridism. Hence, we propose a Hybrid \(L_q\) distance, a Weighted Hybrid \(L_q\) distance, as well as the adaptive version of the Hybrid \(L_q\) distance for interval data. Experiments with synthetic and real interval data sets illustrate the usefulness of the hybrid approach to improve dynamic clustering for interval data.

中文翻译：

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基于混合$$ L_q $$ Lq距离的区间数据动态聚类

动态集群定义了数据中的分区以及每个分区的原型。距离度量负责检查实例与原型之间的紧密度。考虑到有关间隔数据的文献，距离取决于间隔范围，并且忽略了间隔内的信息。本文提出了新的距离，以探索区间内的信息。它还提供了间隔到点的映射，从而保留了它们的空间位置和内部变化。我们基于点数据的已知\（L_q \）距离为间隔数据制定新的混合距离。这个新的距离允许杂交的加权表达。因此，我们提出了一个混合\（L_q \）距离，一个加权混合\（L_q \）距离，以及间隔数据的混合\（L_q \）距离的自适应版本。用合成和实际间隔数据集进行的实验说明了混合方法对于改进间隔数据的动态聚类的有用性。