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

• URL: http://arxiv.org/abs/2309.06634v2
• Date: Mon, 4 Mar 2024 12:08:53 GMT
• Title: $G$-Mapper: Learning a Cover in the Mapper Construction
• Authors: Enrique Alvarado, Robin Belton, Emily Fischer, Kang-Ju Lee, Sourabh Palande, Sarah Percival, Emilie Purvine
• Abstract summary: The Mapper algorithm is a visualization technique in topological data analysis (TDA) that outputs a graph reflecting the structure of a given dataset. We present an algorithm that optimize 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 iteratively applying the Anderson-Darling test.
• Score: 0.7852714805965528
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Mapper algorithm is a visualization technique in topological data analysis (TDA) that outputs a graph reflecting the structure of a given dataset. However, the Mapper algorithm requires tuning several parameters in order to generate a ``nice" Mapper graph. This 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 iteratively applying the Anderson-Darling test. Our splitting procedure employs a Gaussian mixture model to carefully choose the cover according to the distribution of the 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, while also running significantly fast.

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