  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 generic 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 introduce
a construction of 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 generic assumptions. We also illustrate the usability of this
method in simulations.

Algebraic Topology;Combinatorics;Neurons and Cognition;Machine Learning