Research Directions to Validate Topological Models of Multi-Dimensional DataDownload PDF

Oct 10, 2020 (edited Dec 05, 2020)NeurIPS 2020 Workshop TDA and Beyond Blind SubmissionReaders: Everyone
  • 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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