intRinsic: an R Package for Model-Based Estimation of the Intrinsic Dimension of a Dataset

TL;DR

intRinsic is an R package providing advanced likelihood-based estimators for the intrinsic dimension of datasets, aiding in dimensionality reduction and understanding dataset topology through homogeneous and heterogeneous models.

Contribution

The paper introduces novel likelihood-based estimators for intrinsic dimension, implemented in an accessible R package with efficient algorithms for both homogeneous and heterogeneous data.

Findings

Demonstrates estimator performance on simulated datasets

Applies estimators to the Alon microarray dataset

Shows how intrinsic dimension estimates reveal dataset structure

Abstract

This article illustrates intRinsic, an R package that implements novel state-of-the-art likelihood-based estimators of the intrinsic dimension of a dataset, an essential quantity for most dimensionality reduction techniques. In order to make these novel estimators easily accessible, the package contains a small number of high-level functions that rely on a broader set of efficient, low-level routines. Generally speaking, intRinsic encompasses models that fall into two categories: homogeneous and heterogeneous intrinsic dimension estimators. The first category contains the two nearest neighbors estimator, a method derived from the distributional properties of the ratios of the distances between each data point and its first two closest neighbors. The functions dedicated to this method carry out inference under both the frequentist and Bayesian frameworks. In the second category, we find the heterogeneous intrinsic dimension algorithm, a Bayesian mixture model for which an efficient Gibbs sampler is implemented. After presenting the theoretical background, we demonstrate the performance of the models on simulated datasets. This way, we can facilitate the exposition by immediately assessing the validity of the results. Then, we employ the package to study the intrinsic dimension of the Alon dataset, obtained from a famous microarray experiment. Finally, we show how the estimation of homogeneous and heterogeneous intrinsic dimensions allows us to gain valuable insights into the topological structure of a dataset.