Smooth noisy PCA using a 1st 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 paper we develop a smooth version of PCA derived from a maximum likelihood framework. A 1^st 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.