Ball Mapper is an widely used tool in topological data analysis for summarizing the structure of high-dimensional data through metric-based coverings and graph representations. A central computational bottleneck in Ball Mapper is the construction of the underlying cover, which requires repeated range queries to identify data points within a fixed distance of selected landmarks. As data sets grow in size and dimensionality, naive implementations of this step become increasingly inefficient. In this work, we study practical strategies for accelerating cover construction in Ball Mapper by improving the efficiency of range queries. We integrate two complementary approaches into the Ball Mapper pipeline: hierarchical geometric pruning using ball tree data structures, and hardware-aware distance computation using Facebook AI Similarity Search. We describe the underlying algorithms, discuss their trade-offs with respect to metric flexibility and dimensionality, and provide implementation details relevant to large-scale data analysis. Empirical benchmarks demonstrate that both approaches yield substantial speedups over the baseline implementation, with performance gains depending on data set size, dimensionality, and choice of distance function. These results improve the practical scalability of Ball Mapper without modifying its theoretical formulation and provide guidance for the efficient implementation of metric-based exploratory tools in modern data analysis workflows.

翻译：Ball Mapper是拓扑数据分析中广泛使用的工具，通过基于度量的覆盖与图表示来概括高维数据的结构。Ball Mapper的核心计算瓶颈在于底层覆盖的构建，该过程需要反复执行范围查询以识别与选定地标点固定距离内的数据点。随着数据集规模与维度的增长，该步骤的朴素实现效率日益低下。本研究针对通过提升范围查询效率来加速Ball Mapper覆盖构建的实际策略展开探讨。我们将两种互补方法整合至Ball Mapper流程中：基于球树数据结构的层次化几何剪枝，以及利用Facebook AI相似性搜索的硬件感知距离计算。本文阐述了底层算法，讨论了其在度量灵活性与维度方面的权衡，并提供了与大规模数据分析相关的实现细节。实证基准测试表明，两种方法均较基线实现获得显著加速，其性能提升取决于数据集规模、维度及距离函数的选择。这些成果在不改变Ball Mapper理论框架的前提下提升了其实际可扩展性，并为现代数据分析工作流中基于度量的探索性工具的高效实现提供了指导。