Iterative minimal residual method provides optimal regularization parameter for extreme learning machines

Minimal residual method provides optimal regularization parameter for diffuse optical tomography.

The inverse problem in the diffuse optical tomography is known to be nonlinear, ill-posed, and sometimes under-determined, requiring regularization to obtain meaningful results, with Tikhonov-type regularization being the most popular one. The choice of this regularization parameter dictates the reconstructed optical image quality and is typically chosen empirically or based on prior experience...

Parameter-free regularization in Extreme Learning Machines with affinity matrices

This paper proposes a novel regularization approach for Extreme Learning Machines. Regularization is performed using a priori spacial information expressed by an affinity matrix. We show that the use of this type of a priori information is similar to perform Tikhonov regularization. Furthermore, if a parameter free affinity matrix is used, like the cosine similarity matrix, regularization is pe...

An Iterative Method for the Solution of Nonlinear Regularization Problems with Regularization Parameter Estimation

Ill posed problems constitute the mathematical model of a large variety of applications. Aim of this paper is to define an iterative algorithm finding the solution of a regularization problem. The method minimizes a function constituted by a least squares term and a generally nonlinear regularization term, weighted by a regularization parameter. The proposed method computes a sequence of iterat...

Minimal Residual Smoothing in Multi-Level Iterative Method

Minimal Residual Smoothing in Multi-Level Iterative Method

A minimal residual smoothing (MRS) technique is employed to accelerate the convergence of the multi-level iterative method by smoothing the residuals of the original iterative sequence. The sequence with smoothed residuals is reintroduced into the multi-level iterative process. The new sequence generated by this acceleration procedure converges much faster than both the sequence generated by th...