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Found 41 papers, 2 papers with code
Expressing Multivariate Time Series as Graphs with Time Series Attention Transformer
We further visualize the embedded dynamic graphs to illustrate the graph representation power of TSAT.
Multivariate Time Series Forecasting
Representation Learning
+1
Wasserstein Generative Adversarial Uncertainty Quantification in Physics-Informed Neural Networks
In this paper, we study a physics-informed algorithm for Wasserstein Generative Adversarial Networks (WGANs) for uncertainty quantification in solutions of partial differential equations.
Parallel Active Subspace Decomposition for Scalable and Efficient Tensor Robust Principal Component Analysis
Tensor robust principal component analysis (TRPCA) has received a substantial amount of attention in various fields.
Exact Tensor Completion from Sparsely Corrupted Observations via Convex Optimization
This paper conducts a rigorous analysis for provable estimation of multidimensional arrays, in particular third-order tensors, from a random subset of its corrupted entries.
Sparse Kernel Canonical Correlation Analysis via $\ell_1$-regularization
Our algorithm is based on a relationship between kernel CCA and least squares.
Semi-Supervised Low-Rank Mapping Learning for Multi-Label Classification
SLRM model takes advantage of the nuclear norm regularization on mapping to effectively capture the label correlations.
Robust Tensor Completion Using Transformed Tensor SVD
In this paper, we study robust tensor completion by using transformed tensor singular value decomposition (SVD), which employs unitary transform matrices instead of discrete Fourier transform matrix that is used in the traditional tensor SVD.
Framelet Representation of Tensor Nuclear Norm for Third-Order Tensor Completion
In the literature, the tensor nuclear norm can be computed by using tensor singular value decomposition based on the discrete Fourier transform matrix, and tensor completion can be performed by the minimization of the tensor nuclear norm which is the relaxation of the sum of matrix ranks from all Fourier transformed matrix frontal slices.
Bilinear Constraint based ADMM for Mixed Poisson-Gaussian Noise Removal
In this paper, we propose new operator-splitting algorithms for the total variation regularized infimal convolution (TV-IC) model [4] in order to remove mixed Poisson-Gaussian(MPG) noise.
Orthogonal Nonnegative Tucker Decomposition
In this paper, we study the nonnegative tensor data and propose an orthogonal nonnegative Tucker decomposition (ONTD).
Tensor train rank minimization with nonlocal self-similarity for tensor completion
The TT rank minimization accompany with \emph{ket augmentation}, which transforms a lower-order tensor (e. g., visual data) into a higher-order tensor, suffers from serious block-artifacts.
Sparse Nonnegative Tensor Factorization and Completion with Noisy Observations
We propose to minimize the sum of the maximum likelihood estimation for the observations with nonnegativity constraints and the tensor $\ell_0$ norm for the sparse factor.
Nonnegative Low Rank Tensor Approximation and its Application to Multi-dimensional Images
The main aim of this paper is to develop a new algorithm for computing nonnegative low rank tensor approximation for nonnegative tensors that arise in many multi-dimensional imaging applications.
Tensorizing GAN with High-Order Pooling for Alzheimer's Disease Assessment
To the best of our knowledge, the proposed Tensor-train, High-pooling and Semi-supervised learning based GAN (THS-GAN) is the first work to deal with classification on MRI images for AD diagnosis.
Tangent Space Based Alternating Projections for Nonnegative Low Rank Matrix Approximation
In this paper, we develop a new alternating projection method to compute nonnegative low rank matrix approximation for nonnegative matrices.
Dictionary Learning with Low-rank Coding Coefficients for Tensor Completion
In this paper, we propose a novel tensor learning and coding model for third-order data completion.
Non-Local Robust Quaternion Matrix Completion for Color Images and Videos Inpainting
A new patch group based NSS prior scheme is proposed to learn explicit NSS models of natural color images.
Tensor Completion by Multi-Rank via Unitary Transformation
The main aim of this paper is to study $n_1 \times n_2 \times n_3$ third-order tensor completion based on transformed tensor singular value decomposition, and provide a bound on the number of required sample entries.
Approximating Probability Distributions by using Wasserstein Generative Adversarial Networks
Studied here are Wasserstein generative adversarial networks (WGANs) with GroupSort neural networks as their discriminators.
Self-Supervised Nonlinear Transform-Based Tensor Nuclear Norm for Multi-Dimensional Image Recovery
Recently, transform-based tensor nuclear norm minimization methods are considered to capture low-rank tensor structures to recover third-order tensors in multi-dimensional image processing applications.
Co-Separable Nonnegative Matrix Factorization
It aims to find a low rank approximation for nonnegative data M by a product of two nonnegative matrices W and H. In general, NMF is NP-hard to solve while it can be solved efficiently under separability assumption, which requires the columns of factor matrix are equal to columns of the input matrix.
Signal Reconstruction from Phase-only Measurements: Uniqueness Condition, Minimal Measurement Number and Beyond
This paper studies the phase-only reconstruction problem of recovering a complex-valued signal $\textbf{x}$ in $\mathbb{C}^d$ from the phase of $\textbf{Ax}$ where $\textbf{A}$ is a given measurement matrix in $\mathbb{C}^{m\times d}$.
FastHyMix: Fast and Parameter-free Hyperspectral Image Mixed Noise Removal
This paper introduces a fast and parameter-free hyperspectral image mixed noise removal method (termed FastHyMix), which characterizes the complex distribution of mixed noise by using a Gaussian mixture model and exploits two main characteristics of hyperspectral data, namely low-rankness in the spectral domain and high correlation in the spatial domain.
Morphological feature visualization of Alzheimer's disease via Multidirectional Perception GAN
In this work, a novel Multidirectional Perception Generative Adversarial Network (MP-GAN) is proposed to visualize the morphological features indicating the severity of AD for patients of different stages.
Color Image Inpainting via Robust Pure Quaternion Matrix Completion: Error Bound and Weighted Loss
To fill the theoretical vacancy, we obtain the error bound in both clean and corrupted regimes, which relies on some new results of quaternion matrices.
High Dimensional Statistical Estimation under Uniformly Dithered One-bit Quantization
In heavy-tailed regime, while the rates of our estimators become essentially slower, these results are either the first ones in an 1-bit quantized and heavy-tailed setting, or already improve on existing comparable results from some respect.
HessianFR: An Efficient Hessian-based Follow-the-Ridge Algorithm for Minimax Optimization
Wide applications of differentiable two-player sequential games (e. g., image generation by GANs) have raised much interest and attention of researchers to study efficient and fast algorithms.
Error Bound of Empirical $\ell_2$ Risk Minimization for Noisy Standard and Generalized Phase Retrieval Problems
In NGPR, we show $O\big(\|\eta\|\frac{\sqrt{d}}{n}\big)$ for arbitrary $\eta$.
Separable Quaternion Matrix Factorization for Polarization Images
To determine the source factor matrix in quaternion space, we propose a heuristic algorithm called quaternion successive projection algorithm (QSPA) inspired by the successive projection algorithm.
Sparse Nonnegative Tucker Decomposition and Completion under Noisy Observations
In this paper, we propose a sparse nonnegative Tucker decomposition and completion method for the recovery of underlying nonnegative data under noisy observations.
Approximate Secular Equations for the Cubic Regularization Subproblem
In this paper, we propose and analyze a novel CRS solver based on an approximate secular equation, which requires only some of the Hessian eigenvalues and is therefore much more efficient.
A Momentum Accelerated Adaptive Cubic Regularization Method for Nonconvex Optimization
The cubic regularization method (CR) and its adaptive version (ARC) are popular Newton-type methods in solving unconstrained non-convex optimization problems, due to its global convergence to local minima under mild conditions.
Phase Retrieval of Quaternion Signal via Wirtinger Flow
Moreover, we develop a variant of QWF that can effectively utilize a pure quaternion priori (e. g., for color images) by incorporating a quaternion phase factor estimate into QWF iterations.
SVD-PINNs: Transfer Learning of Physics-Informed Neural Networks via Singular Value Decomposition
Physics-informed neural networks (PINNs) have attracted significant attention for solving partial differential equations (PDEs) in recent years because they alleviate the curse of dimensionality that appears in traditional methods.
Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery
To break this barrier, we propose a low-rank tensor function representation (LRTFR), which can continuously represent data beyond meshgrid with infinite resolution.
Quantizing Heavy-tailed Data in Statistical Estimation: (Near) Minimax Rates, Covariate Quantization, and Uniform Recovery
Our major standpoint is that (near) minimax rates of estimation error are achievable merely from the quantized data produced by the proposed scheme.
Quantized Low-Rank Multivariate Regression with Random Dithering
Moreover, we extend our results to a low-rank regression model with matrix responses.
A Parameter-Free Two-Bit Covariance Estimator with Improved Operator Norm Error Rate
By employing dithering scales varying across entries, our estimator enjoys an improved operator norm error rate that depends on the effective rank of the underlying covariance matrix rather than the ambient dimension, thus closing the theoretical gap.
Solving Quadratic Systems with Full-Rank Matrices Using Sparse or Generative Priors
The problem of recovering a signal $\boldsymbol{x} \in \mathbb{R}^n$ from a quadratic system $\{y_i=\boldsymbol{x}^\top\boldsymbol{A}_i\boldsymbol{x},\ i=1,\ldots, m\}$ with full-rank matrices $\boldsymbol{A}_i$ frequently arises in applications such as unassigned distance geometry and sub-wavelength imaging.
On the Expressive Power of a Variant of the Looped Transformer
Previous works try to explain this from the expressive power and capability perspectives that standard transformers are capable of performing some algorithms.
Multispectral Image Restoration by Generalized Opponent Transformation Total Variation
Here opponent transformations for multispectral images are generalized from a well-known opponent transformation for color images.
