Stability of Mapper Graph Invariants

Anonymous

Keywords: Mapper, Graphs, Bootstrapping

TL;DR: We explore the relationship between the sample size and the distributions of structural invariants of Mapper graphs.

Abstract:

Mapper summarizes a large dataset with a smaller graph, which is useful for identifying patterns. However, the Mapper graph may vary widely over different datasets drawn from the same real-world data distribution. In order to use Mapper to make confident conclusions, it is important to have a strong intuition about the algorithm's stability under resampling.

In this paper we perform a case study to explore the empirical convergence properties of Mapper. We build bootstrap samples of different sizes from two real-world datasets, Fashion-MNIST and Wikipedia+Gigaword 5, and construct Mapper graphs from these samples. We then explore the relationship between the sample size and the distributions of structural invariants of these Mapper graphs.

Previous Submission: No