Related papers: Grassmannian diffusion maps based dimension reduct…

Diffusion Generative Models (DGM) have rapidly surfaced as emerging topics in the field of computer vision, garnering significant interest across a wide array of deep learning applications. Despite their high computational demand, these…

Information visualization is essential in making sense out of large data sets. Often, high-dimensional data are visualized as a collection of points in 2-dimensional space through dimensionality reduction techniques. However, these…

We present two graph-based algorithms for multiclass segmentation of high-dimensional data. The algorithms use a diffuse interface model based on the Ginzburg-Landau functional, related to total variation compressed sensing and image…

We propose new algorithms to efficiently average a collection of points on a Grassmannian manifold in both the centralized and decentralized settings. Grassmannian points are used ubiquitously in machine learning, computer vision, and…

This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs. Diffusion distances are used to parametrize low-dimensional structures on the…

Diffusion models have attracted significant attention due to the remarkable ability to create content and generate data for tasks like image classification. However, the usage of diffusion models to generate the high-quality object…

Density-based distances (DBDs) provide a principled approach to metric learning by defining distances in terms of the underlying data distribution. By employing a Riemannian metric that increases in regions of low probability density,…

Predicting the effect of amino acid mutations on enzyme thermodynamic stability (DDG) is fundamental to protein engineering and drug design. While recent deep learning approaches have shown promise, they often process sequence and structure…

This paper addresses the problem of mapping high-dimensional data to a low-dimensional space, in the presence of other known features. This problem is ubiquitous in science and engineering as there are often controllable/measurable features…

We present a novel method for exemplar-based image translation, called matching interleaved diffusion models (MIDMs). Most existing methods for this task were formulated as GAN-based matching-then-generation framework. However, in this…

With the growing interest in foundation models for brain signals, graph-based pretraining has emerged as a promising paradigm for learning transferable representations from connectome data. However, existing contrastive and masked…

We introduce vector diffusion wavelets (VDWs), a novel family of wavelets inspired by the vector diffusion maps algorithm that was introduced to analyze data lying in the tangent bundle of a Riemannian manifold. We show that these wavelets…

A new Riemannian geometry for the Compound Gaussian distribution is proposed. In particular, the Fisher information metric is obtained, along with corresponding geodesics and distance function. This new geometry is applied on a change…

The existence of characteristic structure, or shape, in complex data sets has been recognized as increasingly important for mathematical data analysis. This realization has motivated the development of new tools such as persistent homology…

Recent breakthroughs and rapid integration of generative models (GMs) have sparked interest in the problem of model attribution and their fingerprints. For instance, service providers need reliable methods of authenticating their models to…

The real symplectic Stiefel manifold is the manifold of symplectic bases of symplectic subspaces of a fixed dimension. It features in a large variety of applications in physics and engineering. In this work, we study this manifold with the…

Extracting meaningful information from high-dimensional data poses a formidable modeling challenge, particularly when the data is obscured by noise or represented through different modalities. This research proposes a novel non-parametric…

Nonlinear dimensional reduction with the manifold assumption, often called manifold learning, has proven its usefulness in a wide range of high-dimensional data analysis. The significant impact of t-SNE and UMAP has catalyzed intense…

Diffusion models have emerged as a leading technique for generating images due to their ability to create high-resolution and realistic images. Despite their strong performance, diffusion models still struggle in managing image collections…

This study presents a hierarchical mining framework for high-dimensional imbalanced data, leveraging a depth graph model to address the inherent performance limitations of conventional approaches in handling complex, high-dimensional data…