相关论文: A data-dependent regularization method based on th…

We present a data-assisted iterative regularization method for solving ill-posed inverse problems. The proposed approach, termed \texttt{IRMGL+\(\Psi\)}, integrates classical iterative techniques with a data-driven regularization term…

In this work, we address the solution of both linear and nonlinear ill-posed inverse problems by developing a novel graph-based regularization framework, where the regularization term is formulated through an iteratively updated graph…

We introduce a data-adaptive inversion method that integrates classical or deep learning-based approaches with iterative graph Laplacian regularization, specifically targeting acoustic impedance inversion - a critical task in seismic…

Recent developments in deep learning have revolutionized the paradigm of image restoration. However, its applications on real image denoising are still limited, due to its sensitivity to training data and the complex nature of real image…

In the (special) smoothing spline problem one considers a variational problem with a quadratic data fidelity penalty and Laplacian regularisation. Higher order regularity can be obtained via replacing the Laplacian regulariser with a…

High-dimensional data often exhibit dependencies among variables that violate the isotropic-noise assumption under which principal component analysis (PCA) is optimal. For cases where the noise is not independent and identically distributed…

This paper investigates the use of methods from partial differential equations and the Calculus of variations to study learning problems that are regularized using graph Laplacians. Graph Laplacians are a powerful, flexible method for…

Inverse imaging problems are inherently under-determined, and hence it is important to employ appropriate image priors for regularization. One recent popular prior---the graph Laplacian regularizer---assumes that the target pixel patch is…

Semi-supervised Laplacian regularization, a standard graph-based approach for learning from both labelled and unlabelled data, was recently demonstrated to have an insignificant high dimensional learning efficiency with respect to…

The performance of traditional graph Laplacian methods for semi-supervised learning degrades substantially as the ratio of labeled to unlabeled data decreases, due to a degeneracy in the graph Laplacian. Several approaches have been…

This paper addresses theory and applications of $\ell_p$-based Laplacian regularization in semi-supervised learning. The graph $p$-Laplacian for $p>2$ has been proposed recently as a replacement for the standard ($p=2$) graph Laplacian in…

Bi-stochastic normalization provides an alternative normalization of graph Laplacians in graph-based data analysis and can be computed efficiently by Sinkhorn-Knopp (SK) iterations. This paper proves the convergence of bi-stochastically…

Recommendation algorithm plays an important role in recommendation system (RS), which predicts users' interests and preferences for some given items based on their known information. Recently, a recommendation algorithm based on the graph…

We apply concepts from manifold regularization to develop new regularization techniques for training locally stable deep neural networks. Our regularizers are based on a sparsification of the graph Laplacian which holds with high…

The graph Laplacian regularization term is usually used in semi-supervised representation learning to provide graph structure information for a model $f(X)$. However, with the recent popularity of graph neural networks (GNNs), directly…

In this work we consider a generalized bilevel optimization framework for solving inverse problems. We introduce fractional Laplacian as a regularizer to improve the reconstruction quality, and compare it with the total variation…

Given a weighted graph with $N$ vertices, consider a real-valued regression problem in a semi-supervised setting, where one observes $n$ labeled vertices, and the task is to label the remaining ones. We present a theoretical study of…

In this paper, we develop a novel weighted Laplacian method, which is partially inspired by the theory of graph Laplacian, to study recent popular graph problems, such as multilevel graph partitioning and balanced minimum cut problem, in a…

We tackle the network topology inference problem by utilizing Laplacian constrained Gaussian graphical models, which recast the task as estimating a precision matrix in the form of a graph Laplacian. Recent research \cite{ying2020nonconvex}…

The common graph Laplacian regularizer is well-established in semi-supervised learning and spectral dimensionality reduction. However, as a first-order regularizer, it can lead to degenerate functions in high-dimensional manifolds. The…