  The estimation of the intrinsic dimension of a dataset is a fundamental step
in most dimensionality reduction techniques. This article illustrates
intRinsic, an R package that implements novel state-of-the-art likelihood-based
estimators of the intrinsic dimension of a dataset. In detail, the methods
included in this package are the TWO-NN, Gride, and Hidalgo models. To allow
these novel estimators to be easily accessible, the package contains a few
high-level, intuitive functions that rely on a broader set of efficient,
low-level routines. intRinsic encompasses models that fall into two categories:
homogeneous and heterogeneous intrinsic dimension estimators. The first
category contains the TWO-NN and Gride models. The functions dedicated to these
two methods carry out inference under both the frequentist and Bayesian
frameworks. In the second category we find Hidalgo, a Bayesian mixture model,
for which an efficient Gibbs sampler is implemented. After discussing the
theoretical background, we demonstrate the performance of the models on
simulated datasets. This way, we can assess the results by comparing them with
the ground truth. Then, we employ the package to study the intrinsic dimension
of the Alon dataset, obtained from a famous microarray experiment. We show how
the estimation of homogeneous and heterogeneous intrinsic dimensions allows us
to gain valuable insights about the topological structure of a dataset.
