G-Mapper: Learning a Cover in the Mapper Construction
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929718376267776 |
|---|---|
| author | Alvarado, Enrique Belton, Robin Fischer, Emily Lee, Kang-Ju Palande, Sourabh Percival, Sarah Purvine, Emilie |
| author_facet | Alvarado, Enrique Belton, Robin Fischer, Emily Lee, Kang-Ju Palande, Sourabh Percival, Sarah Purvine, Emilie |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_06634 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | G-Mapper: Learning a Cover in the Mapper Construction Alvarado, Enrique Belton, Robin Fischer, Emily Lee, Kang-Ju Palande, Sourabh Percival, Sarah Purvine, Emilie Machine Learning Algebraic Topology 62R40, 62R07, 68T09, 62H30 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. |
| title | G-Mapper: Learning a Cover in the Mapper Construction |
| topic | Machine Learning Algebraic Topology 62R40, 62R07, 68T09, 62H30 |
| url | https://arxiv.org/abs/2309.06634 |