Persformer: A Transformer Architecture for Topological Machine Learning

arXiv2112.15210MaRDI QIDQ6387123

Author name not available (Why is that?)

Publication date: 30 December 2021

Abstract: One of the main challenges of Topological Data Analysis (TDA) is to extract features from persistent diagrams directly usable by machine learning algorithms. Indeed, persistence diagrams are intrinsically (multi-)sets of points in $mathbb{R}^2$ and cannot be seen in a straightforward manner as vectors. In this article, we introduce $extttPersformer$, the first Transformer neural network architecture that accepts persistence diagrams as input. The $extttPersformer$ architecture significantly outperforms previous topological neural network architectures on classical synthetic and graph benchmark datasets. Moreover, it satisfies a universal approximation theorem. This allows us to introduce the first interpretability method for topological machine learning, which we explore in two examples.

Has companion code repository: https://github.com/giotto-ai/giotto-deep

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