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Many applications in machine learning involve data represented as probability distributions. The emergence of such data requires radically novel techniques to design tractable gradient flows on probability distributions over this type of…

Mesh deformation plays a pivotal role in many 3D vision tasks including dynamic simulations, rendering, and reconstruction. However, defining an efficient discrepancy between predicted and target meshes remains an open problem. A prevalent…

Optimal Transport has sparked vivid interest in recent years, in particular thanks to the Wasserstein distance, which provides a geometrically sensible and intuitive way of comparing probability measures. For computational reasons, the…

In generative modeling, the Wasserstein distance (WD) has emerged as a useful metric to measure the discrepancy between generated and real data distributions. Unfortunately, it is challenging to approximate the WD of high-dimensional…

In generative modeling, the Wasserstein distance (WD) has emerged as a useful metric to measure the discrepancy between generated and real data distributions. Unfortunately, it is challenging to approximate the WD of high-dimensional…

Compared with word embedding based on point representation, distribution-based word embedding shows more flexibility in expressing uncertainty and therefore embeds richer semantic information when representing words. The Wasserstein…

Euclidean representation learning methods have achieved promising results in image fusion tasks, which can be attributed to their clear advantages in handling with linear space. However, data collected from a realistic scene usually has a…

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…

Learning low-dimensional representations from multi-view relational data is challenging when underlying geometries differ across views. We propose Bary-GWMDS, a Gromov-Wasserstein-based method that operates directly on distance matrices to…

Embeddings in machine learning are low-dimensional representations of complex input patterns, with the property that simple geometric operations like Euclidean distances and dot products can be used for classification and comparison tasks.…

Simplicial complexes form an important class of topological spaces that are frequently used in many application areas such as computer-aided design, computer graphics, and simulation. Representation learning on graphs, which are just 1-d…

Since the introduction of the Sliced Wasserstein distance in the literature, its simplicity and efficiency have made it one of the most interesting surrogate for the Wasserstein distance in image processing and machine learning. However,…

We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…

Recently, deep metric learning techniques received attention, as the learned distance representations are useful to capture the similarity relationship among samples and further improve the performance of various of supervised or…

Gaussian mixture models (GMM) are powerful parametric tools with many applications in machine learning and computer vision. Expectation maximization (EM) is the most popular algorithm for estimating the GMM parameters. However, EM…

Word embeddings -- distributed representations of words -- in deep learning are beneficial for many tasks in natural language processing (NLP). However, different embedding sets vary greatly in quality and characteristics of the captured…

Unsupervised learning aims to capture the underlying structure of potentially large and high-dimensional datasets. Traditionally, this involves using dimensionality reduction (DR) methods to project data onto lower-dimensional spaces or…

Different machine learning models can represent the same underlying concept in different ways. This variability is particularly valuable for in-the-wild multimodal retrieval, where the objective is to identify the corresponding…

Graph representation learning is a fast-growing field where one of the main objectives is to generate meaningful representations of graphs in lower-dimensional spaces. The learned embeddings have been successfully applied to perform various…

Learning representations that capture both intrinsic data geometry and target-relevant structure remains a fundamental challenge, particularly in settings where data reduction must balance compression with predictive fidelity. While…