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We introduce diffusion geometry as a new framework for geometric and topological data analysis. Diffusion geometry uses the Bakry-Emery $\Gamma$-calculus of Markov diffusion operators to define objects from Riemannian geometry on a wide…
In this paper, we demonstrate how deterministic and stochastic dynamics on manifolds, as well as differential geometric constructions can be implemented concisely and efficiently using modern computational frameworks that mix symbolic…
In geosciences, the use of classical Euclidean methods is unsuitable for treating and analyzing some types of data, as this may not belong to a vector space. This is the case for correlation matrices, belonging to a subfamily of symmetric…
Geospatial data analysis plays a crucial role in tackling intricate societal challenges such as urban planning and climate modeling. However, employing tools like GeoPandas, a prominent Python library for geospatial data manipulation,…
We introduce novel estimators for computing the curvature, tangent spaces, and dimension of data from manifolds, using tools from diffusion geometry. Although classical Riemannian geometry is a rich source of inspiration for geometric data…
We study a probabilistic numerical method for the solution of both boundary and initial value problems that returns a joint Gaussian process posterior over the solution. Such methods have concrete value in the statistics on Riemannian…
Instance Space Analysis is a methodology to evaluate algorithm performance across diverse problem fields. Through visualisation and exploratory data analysis techniques, Instance Space Analysis offers objective, data-driven insights into…
Machine learning has been progressively generalised to operate within non-Euclidean domains, but geometrically accurate methods for learning on surfaces are still falling behind. The lack of closed-form Riemannian operators, the…
This entry contains the core material of my habilitation thesis, soon to be officially submitted. It provides a self-contained presentation of the original results in this thesis, in addition to their detailed proofs. The motivation of…
Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations…
This paper advocates a novel framework for segmenting a dataset in a Riemannian manifold $M$ into clusters lying around low-dimensional submanifolds of $M$. Important examples of $M$, for which the proposed clustering algorithm is…
Classical archetypal analysis is appealing for its interpretability, but its linear geometry can limit performance on data with strongly non-linear structure; at the same time, existing neural extensions improve flexibility while often…
The study of hidden structures in data presents challenges in modern statistics and machine learning. We introduce the $\mathbf{gips}$ package in R, which identifies permutation subgroup symmetries in Gaussian vectors. $\mathbf{gips}$…
Graph convolutional networks (GCNs) are powerful frameworks for learning embeddings of graph-structured data. GCNs are traditionally studied through the lens of Euclidean geometry. Recent works find that non-Euclidean Riemannian manifolds…
Large or very large spatial (and spatio-temporal) datasets have become common place in many environmental and climate studies. These data are often collected in non-Euclidean spaces (such as the planet Earth) and they often present…
Sparsity-based representations have recently led to notable results in various visual recognition tasks. In a separate line of research, Riemannian manifolds have been shown useful for dealing with features and models that do not lie in…
Simulation of conditioned diffusion processes is an essential tool in inference for stochastic processes, data imputation, generative modelling, and geometric statistics. Whilst simulating diffusion bridge processes is already difficult on…
Optimization over the embedded submanifold defined by constraints $c(x) = 0$ has attracted much interest over the past few decades due to its wide applications in various areas. Plenty of related optimization packages have been developed…
Graph representations of programs are commonly a central element of machine learning for code research. We introduce an open source Python library python_graphs that applies static analysis to construct graph representations of Python…
Bayesian Networks (BNs) are used in various fields for modeling, prediction, and decision making. pgmpy is a python package that provides a collection of algorithms and tools to work with BNs and related models. It implements algorithms for…