$G$-Mapper: Learning a Cover in the Mapper Construction

The Mapper algorithm is a visualization technique in topological data analysis (TDA) that outputs a graph reflecting the structure of a given dataset. The Mapper algorithm requires tuning several parameters in order to generate a "nice" Mapper graph. The paper focuses on selecting the cover parameter. We present an algorithm that optimizes the cover of a Mapper graph by splitting a cover repeatedly according to a statistical test for normality. Our algorithm is based on $G$-means clustering which searches for the optimal number of clusters in $k$-means by conducting iteratively the Anderson-Darling test. Our splitting procedure employs a Gaussian mixture model in order to choose carefully the cover based on the distribution of a given data. Experiments for synthetic and real-world datasets demonstrate that our algorithm generates covers so that the Mapper graphs retain the essence of the datasets.