Vinsamlegast notið þetta auðkenni þegar þið vitnið til verksins eða tengið í það: http://hdl.handle.net/1946/7412
Smooth noisy PCA Using a First Order Roughness Penalty
Principal component analysis (PCA) and other multivariate methods have proven to be useful in a variety of engineering and science fields. PCA is commonly used for dimensionality reduction. PCA has also proven to be useful in functional magnetic resonance imaging (fMRI) research where it is used to decompose the fMRI data into components which can be associated with biological processes. In this thesis, a smooth version of PCA, derived from a maximum likelihood framework, is developed. A first order roughness penalty term is added to the log-likelihood function, which is then maximized for the parameters of interest with an expectation maximization (EM) algorithm. This new method is applied both to simulated data and real fMRI data.
Imposing smoothness is often justifiable. Natural signals are often known to be smooth and all recording devices are susceptible to noise. The proposed method imposes smoothness on the solution within the maximum likelihood framework.
My main contributions to this work has been to derive the proposed method and to develop a EM algorithm that finds the solution. Also, I developed a cross-validation method for determining the smoothness of the result and did a detailed comparison of the proposed method to other PCA methods.