Maria d'Errico

Aldo Glielmo, Iuri Macocco, Diego Doimo et al.

DADApy is a python software package for analysing and characterising high-dimensional data manifolds. It provides methods for estimating the intrinsic dimension and the probability density, for performing density-based clustering and for comparing different distance metrics. We review the main functionalities of the package and exemplify its usage in toy cases and in a real-world application. DADApy is freely available under the open-source Apache 2.0 license.

Elena Facco, Maria d'Errico, Alex Rodriguez et al.

Analyzing large volumes of high-dimensional data is an issue of fundamental importance in data science, molecular simulations and beyond. Several approaches work on the assumption that the important content of a dataset belongs to a manifold whose Intrinsic Dimension (ID) is much lower than the crude large number of coordinates. Such manifold is generally twisted and curved, in addition points on it will be non-uniformly distributed: two factors that make the identification of the ID and its exploitation really hard. Here we propose a new ID estimator using only the distance of the first and the second nearest neighbor of each point in the sample. This extreme minimality enables us to reduce the effects of curvature, of density variation, and the resulting computational cost. The ID estimator is theoretically exact in uniformly distributed datasets, and provides consistent measures in general. When used in combination with block analysis, it allows discriminating the relevant dimensions as a function of the block size. This allows estimating the ID even when the data lie on a manifold perturbed by a high-dimensional noise, a situation often encountered in real world data sets. We demonstrate the usefulness of the approach on molecular simulations and image analysis.

Maria d'Errico, Elena Facco, Alessandro Laio et al.

Data analysis in high-dimensional spaces aims at obtaining a synthetic description of a data set, revealing its main structure and its salient features. We here introduce an approach providing this description in the form of a topography of the data, namely a human-readable chart of the probability density from which the data are harvested. The approach is based on an unsupervised extension of Density Peak clustering and a non-parametric density estimator that measures the probability density in the manifold containing the data. This allows finding automatically the number and the height of the peaks of the probability density, and the depth of the "valleys" separating them. Importantly, the density estimator provides a measure of the error, which allows distinguishing genuine density peaks from density fluctuations due to finite sampling. The approach thus provides robust and visual information about the density peaks' height, their statistical reliability, and their hierarchical organization, offering a conceptually powerful extension of the standard clustering partitions. We show that this framework is particularly useful in the analysis of complex data sets.