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

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.

A global perspective on the intrinsic dimensionality of COVID-19 data

“…A closed-form expression for the posterior distribution is not available, so we rely on Markov Chain Monte Carlo (MCMC) techniques to simulate a posterior sample. The interested reader can find more technical discussions of this model specification and the validity of the underlying hypothesis in the Supplementary Material of related papers 14 , 15 . In these references, one can also find more details about the Gibbs sampler algorithm used for fitting the model and the post-processing tools adopted to deal with computational issues such as label-switching.…”

“…A sparse mixture modelling approach 19 , 20 is employed in this analysis, with mixture components, and for the Dirichlet priors of the mixture weights. Three matrices are produced as the output 15 : Membership labels (dim: ) where each column contains the MCMC sample of the membership labels for every observation; Cluster probabilities (dim: ) where each column contains the MCMC sample of the mixing weights for each mixture component; Intrinsic dimensions (dim: ) where each column contains an MCMC sample for every ID parameter estimated in each cluster. The MCMC chains produced by Hidalgo may exhibit label-switching issues, which prevents direct extraction of inference from the MCMC output.…”

“…This way, we can estimate the number of latent ID manifolds in the dataset. Moreover, we can also obtain more specific results by following a post-processing procedure 15 , devised to address the label-switching issue. The algorithm that is used maps the L different parameter-specific chains – one for each mixture component parameter – to n observation-specific chains .…”

“…Hidalgo extends this framework, allowing the presence of multiple manifolds characterised by different ID values in the same dataset. The Bayesian local ID estimator has been applied successfully to a diverse range of datasets for scenarios such as financial markets, neuroimaging, proteomics 14 , genomics 15 , and high-resolution player tracking data 11 . Here, we seek to organise the pandemic dynamics of different countries into groups with similar ID to help us unveil complex patterns related to the dynamics of the COVID-19 pandemic.…”