Title: Dimension Estimation Using Random Connection Models,
Abstract: Information about intrinsic dimension is crucial to perform dimensionality
reduction, compress information, design efficient algorithms, and do
statistical adaptation. In this paper we propose an estimator for the intrinsic
dimension of a data set. The estimator is based on binary neighbourhood
information about the observations in the form of two adjacency matrices, and
does not require any explicit distance information. The underlying graph is
modelled according to a subset of a specific random connection model, sometimes
referred to as the Poisson blob model. Computationally the estimator scales
like n log n, and we specify its asymptotic distribution and rate of
convergence. A simulation study on both real and simulated data shows that our
approach compares favourably with some competing methods from the literature,
including approaches that rely on distance information.