REGULARIZED LATENT VARIABLE METHODS IN THE PRESENCE OF STRUCTURED NOISE AND THEIR APPLICATION IN THE ANALYSIS OF ELECTROENCEPHALOGRAM DATA

Abstract

<p>This thesis provides new regression methods for the removal of structured noise in datasets. With multivariable data, the variables and the noise can be both temporally correlated (i.e. auto correlated in time) and contemporaneously correlated (i.e. cross-correlated at the same time). In many occasions it is possible to acquire measurements of the noise, or some function of it, during the data collection. Several new constrained latent variable methods (LVM) that are built upon previous LVM regression frameworks are introduced. These methods make use of the additional information available about the noise to decompose a dataset into basis for the noise and signal. The properties of these methods are investigated mathematically, and through both simulation and application to actual biomedical data.</p> <p>In Chapter Two, linear, constrained LVM methods are introduced. The performance of these methods are compared to the other similar LVM methods as well as ordinary PLS throughout several simulation studies. In Chapter Three, a NIPALS type algorithm is developed for the soft constrained PLS method which is also able to account for missing data as well as datasets with large covariance matrices. Chapter Four introduces the nonlinear-kernelized constrained LVM methods. These methods are capable of handling severe nonlinearities in the datasets. The performance of these methods are compared to nonlinear kernel PLS method. In Chapter Five the constrained methods are used to remove ballistocardiographic and muscle artifacts from EEG datasets in combined EEG-fMRI as well as single EEG experiments on patients. The results are shown and compared to the standard noise removal methods used in the field. Finally in Chapter Six, the overall conclusion and scope of the future work is laid out.</p>