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Multiparameter Persistence Images for Topological Machine Learning

Mathieu Carriere 1 Andrew Blumberg 2
1 DATASHAPE - Understanding the Shape of Data
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : In the last decade, there has been increasing interest in topological data analysis, a new methodology for using geometric structures in data for inference and learning. A central theme in the area is the idea of persistence, which in its most basic form studies how measures of shape change as a scale parameter varies. There are now a number of frameworks that support statistics and machine learning in this context. However, in many applications there are several different parameters one might wish to vary: for example, scale and density. In contrast to the one-parameter setting, techniques for applying statistics and machine learning in the setting of multiparameter persistence are not well understood due to the lack of a concise representation of the results. We introduce a new descriptor for multiparameter persistence, which we call the Multiparameter Persistence Image, that is suitable for machine learning and statistical frameworks, is robust to perturbations in the data, has finer resolution than existing descriptors based on slicing, and can be efficiently computed on data sets of realistic size. Moreover, we demonstrate its efficacy by comparing its performance to other multiparameter descriptors on several classification tasks.
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https://hal.inria.fr/hal-03112442
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Submitted on : Saturday, January 16, 2021 - 6:55:44 PM
Last modification on : Wednesday, November 3, 2021 - 9:54:46 AM
Long-term archiving on: : Saturday, April 17, 2021 - 6:21:51 PM

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  • HAL Id : hal-03112442, version 1

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Mathieu Carriere, Andrew Blumberg. Multiparameter Persistence Images for Topological Machine Learning. NeurIPS 2020 - 34th Conference on Neural Information Processing Systems, Dec 2020, Vancouver / Virtuel, Canada. ⟨hal-03112442⟩

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