| Abstract: |
| The Mapper algorithm is a popular exploratory data analysis tool for visualizing the underlying graphical structure of a dataset. The Mapper algorithm involves several user specified parameters that make it possible for any graph to be a Mapper graph. We investigate the question of how likely we are to see specific types of subgraphs within a Mapper graph, when data points are randomly sampled from a continuous probability density function. We provide both theoretical and experimental results for how likely we are to get cyclic subgraphs within a Mapper graph. Additionally, we discuss how we can generalize these probabilistic results and use them as a starting point for a statistical inference framework with Mapper graphs. |
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