intRinsic: an R package for model-based estimation of the intrinsic dimension of a dataset
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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.
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