This paper introduces a new approach to computing an approximate solution of Tikhonov-regularized large-scale ill-posed problems with a general nonlinear regularization operator. The iterative method applies a sequence of projections onto generalized Krylov subspaces using a semi-implicit approach to deal with the nonlinearity in the regularization term. A suitable value of the regularization p...

Extreme learning machine (ELM) has emerged as an efficient and effective learning algorithm for classification and regression tasks. Most of the existing research on the ELMs mainly focus on supervised learning. Recently, researchers have extended ELMs for semi-supervised learning, in which they exploit both the labeled and unlabeled data in order to enhance the learning performances. They have...

Abstract Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems ubiquitous in statistics, machine learning computer vision, however, this perception has not yet received theoretical justification. To fill gap, we prove that com...

A general framework for the regularization of constrained PDEs, also called operator DAEs, is presented. The given procedure works for semi-explicit operator DAEs of first order which includes the Navier-Stokes and other flow equations. This reformulation is a regularization in the sense that a semi-discretization in space leads to a DAE of lower index, i.e., of differentiation index 1 instead ...

In this article, we unveil a new property of linear interference cancellation detectors. Particularly, we focus in this study on the linear parallel interference cancellation (LPIC) detector and show that it exhibits a semi-convergence property. The roots of the semi-convergence behavior of the LPIC detector are clarified and the necessary conditions for its occurrence are determined. In additi...

In this article, our goal is to prove the existence and uniqueness of solution for 1D and 2D semi-linear hyperbolic equations in a bounded domain with a monotone nonlinear term. We use elliptic regularization and a finite difference scheme in time to build the approximate solutions for the semi-linear hyperbolic equations, and we utilize the regularization method together with the monotonicity ...

The L-curve method was developed for the selection of regularization parameters in the solution of discrete systems obtained from ill-posed problems. An analysis of this method is given for selecting a parameter for Tikhonov regularization. This analysis, which is carried out in a semi-discrete, semi-stochastic setting, shows that the L-curve approach yields regularized solutions which fail to ...

In this paper, we propose a general formulation of discrete functional regularization on weighted graphs. This framework can be used to on any multi-dimensional data living on graphs of arbitrary topologies. But, in this work, we focus on the microscopic image segmentation and classification with a semi and unsupervised schemes. Moreover, to provide a fast image segmentation we propose a graph ...

This paper studies the problem of semi-supervised learning from the vector field perspective. Many of the existing work use the graph Laplacian to ensure the smoothness of the prediction function on the data manifold. However, beyond smoothness, it is suggested by recent theoretical work that we should ensure second order smoothness for achieving faster rates of convergence for semisupervised r...