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arXiv · 2309.06634

G-Mapper: Learning a Cover in the Mapper Construction

Enrique Alvarado·Robin Belton·Emily Fischer·Kang-Ju Lee·Sourabh Palande·Sarah Percival·Emilie Purvine
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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 faster than a previous iterative method.

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Enrique Alvarado, Robin Belton, Emily Fischer, Kang-Ju Lee, Sourabh Palande, Sarah Percival, Emilie Purvine. 2023-09-12. G-Mapper: Learning a Cover in the Mapper Construction. https://arxiv.org/abs/2309.06634

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