Keywords: Topological validation, multi-dimensional data, simplicial complexes, mapper, generative models, generative simplicial complex
TL;DR: Research directions to validate the topology of mapper and generative simplicial complexes models related to the data distribution
Abstract: Various topological models of multi-dimensional data have been proposed for different applications. One of the main issues is to evaluate how correct these models are given the stochastic nature of the data source typical of exploratory data analysis and machine learning settings. We propose research directions to validate the quality of the Mapper and the Generative Simplicial Complex, two models that compute simplicial complexes from multi-dimensional data.
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