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The mathematical theory of Krylov subspace methods with a focus on solving systems of linear algebraic equations is given a detailed treatment in this principles-based book. Starting from the idea of projections, Krylov subspace methods are characterised by their orthogonality and minimisation properties. Projections onto highly nonlinear Krylov subspaces(More)
We review the development and extensions of the classical total least squares method and describe algorithms for its generalization to weighted and structured approximation problems. In the generic case, the classical total least squares problem has a unique solution, which is given in analytic form in terms of the singular value decomposition of the data(More)
The minor component analysis (MCA) deals with the recovery of the eigenvector associated to the smallest eigenvalue of the autocorrelation matrix of the input data and is a very important tool for signal processing and data analysis. It is almost exclusively solved by linear neurons. This paper presents a linear neuron endowed with a novel learning law,(More)
The electroencephalogram (EEG) is often contaminated by muscle artifacts. In this paper, a new method for muscle artifact removal in EEG is presented, based on canonical correlation analysis (CCA) as a blind source separation (BSS) technique. This method is demonstrated on a synthetic data set. The method outperformed a low-pass filter with different cutoff(More)
The main purpose of this special issue is to present an overview of the progress of a modeling technique which is known as total least squares (TLS) in computational mathematics and engineering, and as errors-in-variables (EIV) modeling or orthogonal regression in the statistical community. The TLS method is one of several linear parameter estimation(More)
In biomedical signal processing, it is often the case that many sources are mixed into the measured signal. The goal is usually to analyze one or several of them separately. In the case of multichannel measurements, several blind source separation techniques are available for decomposing the signal into its components [e.g., independent component analysis(More)
This paper presents a new computational approach for solving the Regularized Total Least Squares problem. The problem is formulated by adding a quadratic constraint to the Total Least Square minimization problem. Starting from the fact that a quadrat-ically constrained Least Squares problem can be solved via a quadratic eigenvalue problem, an iterative(More)
There has been a growing research interest in brain tumor classification based on proton magnetic resonance spectroscopy (1H MRS) signals. Four research centers within the EU funded INTERPRET project have acquired a significant number of long echo 1H MRS signals for brain tumor classification. In this paper, we present an objective comparison of several(More)
Multimodal approaches are of growing interest in the study of neural processes. To this end much attention has been paid to the integration of electroencephalographic (EEG) and functional magnetic resonance imaging (fMRI) data because of their complementary properties. However, the simultaneous acquisition of both types of data causes serious artifacts in(More)
OBJECTIVE To compare and evaluate ranking, regression and combined machine learning approaches for the analysis of survival data. METHODS The literature describes two approaches based on support vector machines to deal with censored observations. In the first approach the key idea is to rephrase the task as a ranking problem via the concordance index, a(More)