Mapper is a popular topological data analysis method to analyse structure of complex high-dimensional data sets. As the Mapper algorithm can be applied to clustering and feature selection with visualization, it is used in various fields such as biology and chemistry. However, some resolution parameters have to be chosen by the user before applying the Mapper algorithm, and the results are sensitive to the selection. In this paper, we focus on the selection of two resolution parameters, the number of intervals and the overlapping percentage. We propose a new resolution parameter selection method in Mapper based on the ensemble technique. We generate multiple Mapper results under various parameter values and apply the fuzzy clustering ensemble method to combine the results. To evaluate Mapper algorithms including the proposed one, three real data sets are considered. The results demonstrate the superiority of the proposed ensemble Mapper method.

中文翻译：

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集成映射器

Mapper 是一种流行的拓扑数据分析方法，用于分析复杂的高维数据集的结构。由于 Mapper 算法可以应用于聚类和具有可视化的特征选择，因此它被用于生物学和化学等各个领域。但是，在应用Mapper算法之前，用户必须选择一些分辨率参数，并且结果对选择很敏感。在本文中，我们关注两个分辨率参数的选择，间隔数和重叠百分比。我们在 Mapper 中基于集成技术提出了一种新的分辨率参数选择方法。我们在各种参数值下生成多个 Mapper 结果，并应用模糊聚类集成方法来组合结果。为了评估 Mapper 算法，包括提议的算法，考虑了三个真实数据集。结果证明了所提出的集成映射器方法的优越性。