Optimal transport (OT) theory can be informally described using the words of the French
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …

Variational problems that involve Wasserstein distances have been recently proposed to
summarize and learn from probability measures. Despite being conceptually simple, such …

We consider in this paper the dictionary learning problem when the observations are
normalized histograms of features. This problem can be tackled using non-negative matrix …

This paper presents a unified framework for smooth convex regularization of discrete optimal
transport problems. In this context, the regularized optimal transport turns out to be …

Variational problems that involve Wasserstein distances and more generally optimal
transport (OT) theory are playing an increasingly important role in data sciences. Such …

Optimal Transport is a useful metric to compare probability distributions and to compute a
pairing given a ground cost. Its entropic regularization variant (eOT) is crucial to have fast …

Many spectral unmixing methods rely on the non-negative decomposition of spectral data
onto a dictionary of spectral templates. In particular, state-of-the-art music transcription …

Optimal transport (OT) distances between probability distributions are parameterized by the
ground metric they use between observations. Their relevance for real-life applications …

We consider the block coordinate descent methods of Gauss-Seidel type with proximal
regularization (BCD-PR), which is a classical method of minimizing general nonconvex …

Extracting relevant urban patterns from multiple data sources can be difficult using classical
clustering algorithms since we have to make a suitable setup of the hyperparameters of the …