Flavia Esposito

T-ARC: Topology-Aware Randomized Clustering via Distributionally Robust Stochastic Block Models

In this work, we introduce a new clustering method, namely T-ARC (Topology-Aware Randomized Clustering), that corrects the geometric bias of K-means by embedding topological information directly into the optimization objective. Building on the assumption that the data admits an underlying hidden structure modeled via a...

Optimization on the Oblique Manifold for Sparse Simplex Constraints via Multiplicative Updates

This work proposes a novel manifold optimization approach that leverages the geometry of oblique manifolds to reformulate the problem and introduces a new Riemannian optimization method based on Riemannian gradient descent that strictly maintains the simplex constraints.

Computational and Applied Mathematics