The paper introduces compact representations called sliced Wasserstein sketches that enable efficient, geometrically meaningful comparisons of probability distributions. It presents an exact decomposition of the squared distance error into residual and partition‑mismatch components, providing computable error certificates for any centroid sketch. Experiments demonstrate that optimal sketches reduce storage while maintaining classification performance, improve generalization with limited labels, and can be used as compact pooling layers in end‑to‑end learning.
arXiv:2605. 14981v2 Announce Type: replace Abstract: Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system.
The paper introduces LOT Wassmap, an algorithm designed to uncover low‑dimensional structures in the Wasserstein space without computing a full pairwise distance matrix. It leverages approximation schemes such as Sinkhorn distances and linearized optimal transport to accelerate computations, and provides theoretical guarantees on embedding quality even when only finite samples are available. Experiments show that LOT Wassmap achieves accurate embeddings that improve with larger sample sizes while significantly reducing computational cost compared to traditional pairwise‑distance‑based methods.
arXiv:2608. 11016v1 Announce Type: cross Abstract: Clustering is a fundamental class of data analysis techniques with the most important representatives being centroid-based methods like $k$-means.
Clustering is a fundamental class of data analysis techniques with the most important representatives being centroid-based methods like $k$-means. Such methods are strongly connected to quantization problems, which aim to approximate general probability measures with discrete ones.
arXiv:2606. 30310v1 Announce Type: cross Abstract: The Sliced Wasserstein (SW) distance has emerged as a computationally attractive alternative to the Wasserstein distance by leveraging one-dimensional optimal transport along random projections.
This paper examines how metric adjustments to Multidimensional Scaling (MDS) can enhance its effectiveness as a visual tool for pattern recognition. The distance under consideration, referred to as Max-D-SW, is an adjustment of the Max-Sliced Wasserstein distance.
arXiv:2610. 20743v1 Announce Type: new Abstract: Many modern learning problems require comparing probability distributions whose individual observations are themselves probability measures, naturally giving rise to meta-measures in $\mathcal{P}(\mathcal{P}(\Omega))$.
arXiv:2605. 09916v2 Announce Type: replace-cross Abstract: We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal transport in large-scale, non-Euclidean datasets.
This paper introduces the Sierpiński-Knopp (SK) Wasserstein distance, a fast metric between persistence diagrams. The SK-Wasserstein distance, denoted $d_{\mathrm{SK}}$, maps diagram points and their...
arXiv:2505. 06835v5 Announce Type: replace Abstract: Sliced optimal transport (SOT), or sliced Wasserstein (SW) distance, is widely recognized for its statistical and computational scalability.
arXiv:2609. 02155v1 Announce Type: new Abstract: The Johnson-Lindenstrauss (JL) lemma guarantees that a random projection of $n$ points to $m=O(\varepsilon^{-2}\log n)$ dimensions preserves pairwise squared distances within relative error $\varepsilon$ with high probability, and this dimension order is asymptotically optimal.
arXiv:2609. 01528v1 Announce Type: cross Abstract: This paper introduces the Sierpi\'nski-Knopp (SK) Wasserstein distance, a fast metric between persistence diagrams.