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

We address the estimation problem for general finite mixture models, with a particular focus on the elliptical mixture models (EMMs). Compared to the widely adopted Kullback-Leibler divergence, we show that the Wasserstein distance provides…

In the Wireless Localization Matching Problem (WLMP) the challenge is to match pieces of equipment with a set of candidate locations based on wireless signal measurements taken by the pieces of equipment. This challenge is complicated by…

Learning energy-based model (EBM) requires MCMC sampling of the learned model as an inner loop of the learning algorithm. However, MCMC sampling of EBMs in high-dimensional data space is generally not mixing, because the energy function,…

Time-lapse electrical resistivity tomography (ERT) is a popular geophysical method to estimate three-dimensional (3D) permeability fields from electrical potential difference measurements. Traditional inversion and data assimilation methods…

A novel method, named Curvature-Augmented Manifold Embedding and Learning (CAMEL), is proposed for high dimensional data classification, dimension reduction, and visualization. CAMEL utilizes a topology metric defined on the Riemannian…

Learning a distance function or metric on a given data manifold is of great importance in machine learning and pattern recognition. Many of the previous works first embed the manifold to Euclidean space and then learn the distance function.…

Deep metric learning (DML) involves training a network to learn a semantically meaningful representation space. Many current approaches mine n-tuples of examples and model interactions within each tuplets. We present a novel, compositional…

We present a new nonlinear dimensionality reduction method, MAPLE, that enhances UMAP by improving manifold modeling. MAPLE employs a self-supervised learning approach to more efficiently encode low-dimensional manifold geometry. Central to…

Understanding and representing the structure of 3D objects in an unsupervised manner remains a core challenge in computer vision and graphics. Most existing unsupervised keypoint methods are not designed for unconditional generative…

This paper introduces a comprehensive unified framework for constructing multi-view diffusion geometries through intertwined multi-view diffusion trajectories (MDTs), a class of inhomogeneous diffusion processes that iteratively combine the…

Masked diffusion models (MDMs) have achieved notable progress in modeling discrete data, while their potential in molecular generation remains underexplored. In this work, we explore their potential and introduce the surprising result that…

Deep learning (DL) based semantic segmentation methods have achieved excellent performance in biomedical image segmentation, producing high quality probability maps to allow extraction of rich instance information to facilitate good…

Latent Diffusion Models (LDM), a subclass of diffusion models, mitigate the computational complexity of pixel-space diffusion by operating within a compressed latent space constructed by Variational Autoencoders (VAEs), demonstrating…

Deep Metric Learning algorithms aim to learn an efficient embedding space to preserve the similarity relationships among the input data. Whilst these algorithms have achieved significant performance gains across a wide plethora of tasks,…

Discrete diffusion models have recently shown great promise for modeling complex discrete data, with masked diffusion models (MDMs) offering a compelling trade-off between quality and generation speed. MDMs denoise by progressively…

Recent masked diffusion models (MDMs) have shown competitive performance compared to autoregressive models (ARMs) for language modeling. While most literature has focused on performance enhancing sampling procedures, efficient sampling from…

We present a variational autoencoder framework for learning and generating configurations of structured polymer globules from distance matrices. We used coarse-grained molecular dynamics to sample polyethylene structures, which we used as…

Low-dimensional embeddings are widely used as visual summaries of high-dimensional data and to enable downstream scientific discoveries. Yet, popular nonlinear dimension reduction methods, such as t-SNE and UMAP, are often selected based on…

Manifold theory has been the central concept of many learning methods. However, learning modern CNNs with manifold structures has not raised due attention, mainly because of the inconvenience of imposing manifold structures onto the…

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…