Efficient Cover Construction for Ball Mapper via Accelerated Range Queries

TL;DR

This paper enhances the efficiency of the Ball Mapper algorithm in topological data analysis by integrating hierarchical pruning and hardware-aware distance computations, significantly speeding up cover construction for large, high-dimensional datasets.

Contribution

It introduces practical strategies combining ball trees and optimized distance calculations to accelerate cover construction in Ball Mapper without altering its theoretical basis.

Findings

Substantial speedups in cover construction times.

Performance improvements depend on dataset size and dimensionality.

Guidelines for implementing efficient metric-based data analysis tools.

Abstract

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.