Related papers: Earthmover-based manifold learning for analyzing m…

We consider the problem of recovering a $d-$dimensional manifold $\mathcal{M} \subset \mathbb{R}^n$ when provided with noiseless samples from $\mathcal{M}$. There are many algorithms (e.g., Isomap) that are used in practice to fit manifolds…

This work introduces a diffusion model for molecule generation in 3D that is equivariant to Euclidean transformations. Our E(3) Equivariant Diffusion Model (EDM) learns to denoise a diffusion process with an equivariant network that jointly…

We develop a diffusion-based approach for various document layout sequence generation. Layout sequences specify the contents of a document design in an explicit format. Our novel diffusion-based approach works in the sequence domain rather…

Euclidean distance matrices (EDMs) are a major tool for localization from distances, with applications ranging from protein structure determination to global positioning and manifold learning. They are, however, static objects which serve…

This paper presents a novel theoretical measure, $\mu^{\text{EMD}}$, based on the Earth Mover's Distance, for quantifying the density shift caused by electronic excitations in molecules. As input, the EMD metric uses only the discretized…

Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central…

Chamfer Distance (CD) and Earth Mover's Distance (EMD) are two broadly adopted metrics for measuring the similarity between two point sets. However, CD is usually insensitive to mismatched local density, and EMD is usually dominated by…

A fundamental task in data exploration is to extract simplified low dimensional representations that capture intrinsic geometry in data, especially for faithfully visualizing data in two or three dimensions. Common approaches to this task…

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…

The performance of optimization-based robot motion planning algorithms is highly dependent on the initial solutions, commonly obtained by running a sampling-based planner to obtain a collision-free path. However, these methods can be slow…

The earth mover's distance (EMD) is a well-known metric on spaces of histograms; roughly speaking, the EMD measures the minimum amount of work required to equalize two histograms. The EMD has a natural generalization that compares an…

Many machine learning problems involve regressing variables on a non-Euclidean manifold -- e.g. a discrete probability distribution, or the 6D pose of an object. One way to tackle these problems through gradient-based learning is to use a…

Distance metric learning (DML) approaches learn a transformation to a representation space where distance is in correspondence with a predefined notion of similarity. While such models offer a number of compelling benefits, it has been…

Existing deep embedding methods in vision tasks are capable of learning a compact Euclidean space from images, where Euclidean distances correspond to a similarity metric. To make learning more effective and efficient, hard sample mining is…

While diffusion models can learn complex distributions, sampling requires a computationally expensive iterative process. Existing distillation methods enable efficient sampling, but have notable limitations, such as performance degradation…

In this paper, we propose a novel self-supervised representation learning method, Self-EMD, for object detection. Our method directly trained on unlabeled non-iconic image dataset like COCO, instead of commonly used iconic-object image…

Nonlinear manifold learning algorithms, such as diffusion maps, have been fruitfully applied in recent years to the analysis of large and complex data sets. However, such algorithms still encounter challenges when faced with real data. One…

Computational elucidation of membrane protein (MP) structures is challenging partially due to lack of sufficient solved structures for homology modeling. Here we describe a high-throughput deep transfer learning method that first predicts…

Although ubiquitous in the sciences, histogram data have not received much attention by the Deep Learning community. Whilst regression and classification tasks for scalar and vector data are routinely solved by neural networks, a principled…

Distance metric learning can be viewed as one of the fundamental interests in pattern recognition and machine learning, which plays a pivotal role in the performance of many learning methods. One of the effective methods in learning such a…