Relative errors versus residuals of approximate solutions of weighted least squares problems in Hilbert space

Robust solutions to uncertain weighted least squares problems ∗

Robust optimization is a rapidly developing methodology for handling optimization problems affected by non-stochastic uncertain-but-bounded data perturbations. In this paper, we consider the weighted least squares problems where the coefficient matrices and vector belong to different uncertain bounded sets. We introduce the robust counterparts of these problems and reformulate them as the tract...

Kernel Partial Least Squares Regression in Reproducing Kernel Hilbert Space

A family of regularized least squares regression models in a Reproducing Kernel Hilbert Space is extended by the kernel partial least squares (PLS) regression model. Similar to principal components regression (PCR), PLS is a method based on the projection of input (explanatory) variables to the latent variables (components). However, in contrast to PCR, PLS creates the components by modeling th...

Spectral compression: Weighted principal component analysis versus weighted least squares

Two weighted compression schemes, Weighted Least Squares (wLS) and Weighted Principal Component Analysis (wPCA), are compared by considering their performance in minimizing both spectral and colorimetric errors of reconstructed reflectance spectra. A comparison is also made among seven different weighting functions incorporated into ordinary PCA/LS to give selectively more importance to the wav...

Approximate Simulation-Based Solution of Large-Scale Least Squares Problems

We consider linear least squares problems of very large dimension, such as those arising for example in inverse problems. We introduce an associated approximate problem, within a subspace spanned by a relatively small number of basis functions, and solution methods that use simulation, importance sampling, and low-dimensional calculations. The main components of this methodology are a regressio...

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations