9 citations · 15 across the 5 of their papers we have counts for
5 papers
Parsimonious Gaussian mixture models with piecewise-constant eigenvalue profiles
Tom Szwagier, Pierre-Alexandre Mattei, Charles Bouveyron +1
Gaussian mixture models (GMMs) are ubiquitous in statistical learning, particularly for unsupervised problems. While full GMMs suffer from the overparameterization of their covaria…
Eigengap Sparsity for Covariance Parsimony
Tom Szwagier, Guillaume Olikier, Xavier Pennec
Covariance estimation is a central problem in statistics. An important issue is that there are rarely enough samples to accurately estimate the coefficients in di…
Nested subspace learning with flags
Tom Szwagier, Xavier Pennec
Many machine learning methods look for low-dimensional representations of the data. The underlying subspace can be estimated by first choosing a dimension and then optimizing a…
Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures
Mathilde Papillon, Sophia Sanborn, Johan Mathe +8
The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern mach…
The curse of isotropy: from principal components to principal subspaces
Tom Szwagier, Xavier Pennec
Principal component analysis is a ubiquitous tool in exploratory data analysis. It is widely used by applied scientists for visualization and interpretability purposes. We raise an…