Related papers: LLE with low-dimensional neighborhood representati…
Given any domain $X\subseteq \mathbb{R}^d$ and a probability measure $\rho$ on $X$, we study the problem of approximating in $L^2(X,\rho)$ a given function $u:X\to\mathbb{R}$, using its noiseless pointwise evaluations at random samples. For…
Low-Light Enhancement (LLE) is aimed at improving the quality of photos/videos captured under low-light conditions. It is worth noting that most existing LLE methods do not take advantage of geometric modeling. We believe that incorporating…
We consider estimating a random vector from its noisy projections onto low dimensional subspaces constituting a fusion frame. A fusion frame is a collection of subspaces, for which the sum of the projection operators onto the subspaces is…
We present a novel framework for learning cost-efficient latent representations in problems with high-dimensional state spaces through nonlinear dimension reduction. By enriching linear state approximations with low-order polynomial terms…
t-distributed stochastic neighbor embedding (t-SNE) is a well-established visualization method for complex high-dimensional data. However, the original t-SNE method is nonparametric, stochastic, and often cannot well prevserve the global…
Unsupervised text embedding methods, such as Skip-gram and Paragraph Vector, have been attracting increasing attention due to their simplicity, scalability, and effectiveness. However, comparing to sophisticated deep learning architectures…
We propose a novel locally adaptive learning estimator for enhancing the inter- and intra- discriminative capabilities of Deep Neural Networks, which can be used as improved loss layer for semantic image segmentation tasks. Most loss layers…
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…
For three decades, carrier-phase observations have been used to obtain the most accurate location estimates using global navigation satellite systems (GNSS). These estimates are computed by minimizing a nonlinear mixed-integer least-squares…
Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…
We study how much a linear program (LP) can be compressed when solved repeatedly, given prior knowledge about its objective function. Existing data-driven projection methods learn low-dimensional surrogate LPs with approximate…
Low-light image enhancement (LLIE) aims to improve the illuminance of images due to insufficient light exposure. Recently, various lightweight learning-based LLIE methods have been proposed to handle the challenges of unfavorable prevailing…
Solving the global method of Weighted Least Squares (WLS) model in image filtering is both time- and memory-consuming. In this paper, we present an alternative approximation in a time- and memory- efficient manner which is denoted as…
Diffusion-based inverse algorithms have shown remarkable performance across various inverse problems, yet their reliance on numerous denoising steps incurs high computational costs. While recent developments of fast diffusion ODE solvers…
We present a new approach to 3D object representation where a neural network encodes the geometry of an object directly into the weights and biases of a second 'mapping' network. This mapping network can be used to reconstruct an object by…
Neural models learn representations of high-dimensional data on low-dimensional manifolds. Multiple factors, including stochasticities in the training process, model architectures, and additional inductive biases, may induce different…
This study investigates the robustness of graph embedding methods for community detection in the face of network perturbations, specifically edge deletions. Graph embedding techniques, which represent nodes as low-dimensional vectors, are…
In contrast to RNNs, which compress their history into a single hidden state, Transformers can attend to all past tokens directly. However, standard Transformers rely solely on the hidden state from the previous layer to represent the…
In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential…
In [L. Chen and R. Li, Journal of Scientific Computing, Vol. 68, pp. 1172--1197, (2016)], an integrated linear reconstruction was proposed for finite volume methods on unstructured grids. However, the geometric hypothesis of the mesh to…