Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein Projection
H Van Assel, C Vincent-Cuaz, N Courty… - ar**
Clustering is a fundamental task in machine learning and data science, and similarity graph-
based clustering is an important approach within this domain. Doubly stochastic symmetric …
based clustering is an important approach within this domain. Doubly stochastic symmetric …
Entropic Optimal Transport Eigenmaps for Nonlinear Alignment and Joint Embedding of High-Dimensional Datasets
Embedding high-dimensional data into a low-dimensional space is an indispensable
component of data analysis. In numerous applications, it is necessary to align and jointly …
component of data analysis. In numerous applications, it is necessary to align and jointly …
Neuc-MDS: Non-Euclidean Multidimensional Scaling Through Bilinear Forms
We introduce Non-Euclidean-MDS (Neuc-MDS), an extension of classical Multidimensional
Scaling (MDS) that accommodates non-Euclidean and non-metric inputs. The main idea is …
Scaling (MDS) that accommodates non-Euclidean and non-metric inputs. The main idea is …
Optimal Transport with Adaptive Regularisation
Regularising the primal formulation of optimal transport (OT) with a strictly convex term leads
to enhanced numerical complexity and a denser transport plan. Many formulations impose a …
to enhanced numerical complexity and a denser transport plan. Many formulations impose a …
A dimensionality reduction technique based on the Gromov-Wasserstein distance
Analyzing relationships between objects is a pivotal problem within data science. In this
context, Dimensionality reduction (DR) techniques are employed to generate smaller and …
context, Dimensionality reduction (DR) techniques are employed to generate smaller and …