A topological approach to inferring the intrinsic dimension of convex sensing data

Min Chun Wu, Vladimir Itskov

Research output: Contribution to journalArticlepeer-review


We consider a common measurement paradigm, where an unknown subset of an affine space is measured by unknown continuous quasi-convex functions. Given the measurement data, can one determine the dimension of this space? In this paper, we develop a method for inferring the intrinsic dimension of the data from measurements by quasi-convex functions, under natural assumptions. The dimension inference problem depends only on discrete data of the ordering of the measured points of space, induced by the sensor functions. We construct a filtration of Dowker complexes, associated to measurements by quasi-convex functions. Topological features of these complexes are then used to infer the intrinsic dimension. We prove convergence theorems that guarantee obtaining the correct intrinsic dimension in the limit of large data, under natural assumptions. We also illustrate the usability of this method in simulations.

Original languageEnglish (US)
Pages (from-to)127-176
Number of pages50
JournalJournal of Applied and Computational Topology
Issue number1
StatePublished - Mar 2022

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Computational Mathematics
  • Geometry and Topology


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