Related papers: The Joint Gromov Wasserstein Objective for Multipl…

Gaussian mixture models find their place as a powerful tool, mostly in the clustering problem, but with proper preparation also in feature extraction, pattern recognition, image segmentation and in general machine learning. When faced with…

This paper considers the problem of estimating a matrix that encodes pairwise distances in a finite metric space (or, more generally, the edge weight matrix of a network) under the barycentric coding model (BCM) with respect to the…

We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity measure or distance between two Hidden Markov Models with state conditional distributions being Gaussian. For such HMMs, the marginal distribution at any…

The Gromov-Wasserstein distance is a notable extension of optimal transport. In contrast to the classic Wasserstein distance, it solves a quadratic assignment problem that minimizes the pair-wise distance distortion under the transportation…

Classical optimal transport problem seeks a transportation map that preserves the total mass betwenn two probability distributions, requiring their mass to be the same. This may be too restrictive in certain applications such as color or…

Gromov-Wasserstein distances are generalization of Wasserstein distances, which are invariant under distance preserving transformations. Although a simplified version of optimal transport in Wasserstein spaces, called linear optimal…

We study rates of convergence for estimation of the Gromov-Wasserstein (GW) distance. For two marginals supported on compact subsets of $\R^{d_x}$ and $\R^{d_y}$, respectively, with $\min \{ d_x,d_y \} > 4$, prior work established the rate…

Analyzing relationships between objects is a pivotal problem within data science. In this context, Dimensionality reduction (DR) techniques are employed to generate smaller and more manageable data representations. This paper proposes a new…

The Gromov-Hausdorff (GH) distance is traditionally used for measuring distances between metric spaces. It is defined as the minimal distortion of embedding one surface into the other, while the optimal correspondence can be described as…

We present an approach for jointly matching and segmenting object instances of the same category within a collection of images. In contrast to existing algorithms that tackle the tasks of semantic matching and object co-segmentation in…

Computational difficulty of quadratic matching and the Gromov-Wasserstein distance has led to various approximation and relaxation schemes. One of such methods, relying on the notion of distance profiles, has been widely used in practice,…

Supervised graph prediction addresses regression problems where the outputs are structured graphs. Although several approaches exist for graph-valued prediction, principled uncertainty quantification remains limited. We propose a conformal…

Single-cell genomics has significantly advanced our understanding of cellular behavior, catalyzing innovations in treatments and precision medicine. However, single-cell sequencing technologies are inherently destructive and can only…

Not identical but similar objects are ubiquitous in our world, ranging from four-legged animals such as dogs and cats to cars of different models and flowers of various colors. This study addresses a novel task of matching such…

Detecting tiny objects is a very challenging problem since a tiny object only contains a few pixels in size. We demonstrate that state-of-the-art detectors do not produce satisfactory results on tiny objects due to the lack of appearance…

This paper studies the optimization of the KL functional on the Wasserstein space of probability measures, and develops a sampling framework based on Wasserstein gradient descent (WGD). We identify two important subclasses of the…

Pairwise comparison of graphs is key to many applications in Machine learning ranging from clustering, kernel-based classification/regression and more recently supervised graph prediction. Distances between graphs usually rely on…

The Wasserstein space of probability measures is known for its intricate Riemannian structure, which underpins the Wasserstein geometry and enables gradient flow algorithms. However, the Wasserstein geometry may not be suitable for certain…

Cross-domain alignment between two sets of entities (e.g., objects in an image, words in a sentence) is fundamental to both computer vision and natural language processing. Existing methods mainly focus on designing advanced attention…

Aligning EM density maps and fitting atomic models are essential steps in single particle cryogenic electron microscopy (cryo-EM), with recent methods leveraging various algorithms and machine learning tools. As aligning maps remains…