Related papers: Structure-Preserving Multi-View Embedding Using Gr…

Learning low-dimensional numerical representations from symbolic data, e.g., embedding the nodes of a graph into a geometric space, is an important concept in machine learning. While embedding into Euclidean space is common, recent…

Extracting insight from the enormous quantity of data generated from molecular simulations requires the identification of a small number of collective variables whose corresponding low-dimensional free-energy landscape retains the essential…

The Gromov-Wasserstein (GW) distance is an extension of the optimal transport problem that allows one to match objects between incomparable spaces. At its core, the GW distance is specified as the solution of a non-convex quadratic program…

Gromov-Wasserstein (GW) distance is a powerful tool for comparing and aligning probability distributions supported on different metric spaces. Recently, GW has become the main modeling technique for aligning heterogeneous data for a wide…

Comparing metric measure spaces (i.e. a metric space endowed with aprobability distribution) is at the heart of many machine learning problems. The most popular distance between such metric measure spaces is theGromov-Wasserstein (GW)…

3D Gaussian Splatting has recently emerged as an efficient solution for high-quality and real-time novel view synthesis. However, its capability for accurate surface reconstruction remains underexplored. Due to the discrete and unstructured…

Inspired by the Kantorovich formulation of optimal transport distance between probability measures on a metric space, Gromov-Wasserstein (GW) distances comprise a family of metrics on the space of isomorphism classes of metric measure…

Predicting commuting flows based on infrastructure and land-use information is critical for urban planning and public policy development. However, it is a challenging task given the complex patterns of commuting flows. Conventional models,…

We present a dynamic subspace approach for efficiently approximating large-scale systems by learning time-continuous trajectories on the Grassmannian manifold. By parameterizing a low-dimensional basis as a geodesic path, the method allows…

We present a framework for building unsupervised representations of entities and their compositions, where each entity is viewed as a probability distribution rather than a vector embedding. In particular, this distribution is supported…

Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions. Here we consider an alternative, which embeds data as discrete…

Generative Design (GD) combines artificial intelligence (AI), physics-based modeling, and multi-objective optimization to autonomously explore and refine engineering designs. Despite its promise in aerospace, automotive, and other…

We study distribution-on-distribution regression problems in which a response distribution depends on multiple distributional predictors. Such settings arise naturally in applications where the outcome distribution is driven by several…

Dimensionality reduction techniques map data represented on higher dimensions onto lower dimensions with varying degrees of information loss. Graph dimensionality reduction techniques adopt the same principle of providing latent…

Deep generative models are tremendously successful in learning low-dimensional latent representations that well-describe the data. These representations, however, tend to much distort relationships between points, i.e. pairwise distances…

One of the key challenges in learning joint embeddings of multiple modalities, e.g. of images and text, is to ensure coherent cross-modal semantics that generalize across datasets. We propose to address this through joint Gaussian…

Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability…

Graph embeddings are low dimensional representations of nodes, edges or whole graphs. Such representations allow for data in a network format to be used along with machine learning models for a variety of tasks (e.g., node classification),…

Multimodal data provide complementary information of a natural phenomenon by integrating data from various domains with very different statistical properties. Capturing the intra-modality and cross-modality information of multimodal data is…

A simple framework Probabilistic Multi-view Graph Embedding (PMvGE) is proposed for multi-view feature learning with many-to-many associations so that it generalizes various existing multi-view methods. PMvGE is a probabilistic model for…