Author Description

This dissertation, "New Algorithms in Factor Analysis: Applications, Model Selection and Findings in Bioinformatics" by Ho-chun, Wu,, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Advancements in microelectronic devices and computational and storage technologies enable the collection of high volume, high speed and high dimension data in many applications. Due to the high dimensionality of these measurements, exact dependence of the observations on the various parameters or variables may not be exactly known. Factor analysis (FA) is a useful multivariate technique to exploit the redundancies among observations and reveal their dependence to some latent variables called factors. Some major issues of the conventional FA are high arithmetic complexity for real-time online implementation, assumption of static system parameters, the demand of interval forecasting, robustness against outlying observations and model selection in problems with high dimension but low number of samples (HDLS). This thesis addresses these issues and proposes new extensions to the existing FA algorithms. First, in order to reduce the arithmetic complexity, we propose new recursive FA algorithms (RFA) that recursively compute only the dominant Principal Components (PCs) and eigenvalues in the major subspace tracked by efficient subspace tracking algorithms. Specifically, two new approaches are proposed for updating the PCs and eigenvalues in the classical fault detection problem with different tradeoff between accuracy and arithmetic complexity, namely rank-1 modification and deflation. They significantly reduce the online arithm