| This thesis consists of two parts: object oriented data analysis of cell images, and analysis of elastic functions. Both topics are motivated by studies in cell culture biology.;The first part discusses object oriented data analysis (OODA) of cell images, which highlights a common critical issue—choice of data objects. OODA is a useful method for analyzing populations of complicated objects, such as images, trees, etc. Instead of naively choosing either the individual cells or the wells (a container in which the cells are grown) as data objects, a new type of data object is proposed, that is the union of a well with its corresponding set of cells. This research suggests that OODA is not simply a framework for understanding the structure of the data analysis. It leads to useful interdisciplinary discussion that gives better results through more appropriate choice of data objects, especially for complex data analyses.;The second part discusses functional data analysis motivated by analyzing data variability among cell growth curves. There are two important types of variation: the horizontal (or phase) variation and the vertical (or amplitude) variation. They can be separated and modeled through a novel domain warping (or curve registration) approach based on the Fisher Rao metric. A convenient square-root velocity function (SRVF) representation is used to computationally simplify the Fisher Rao framework. In this thesis, both separate and joint analyses of these two types of variation are discussed. Compared with conventional approaches such as functional principal component analysis, the SRVF approaches proposed in this thesis can be more efficient and interpretable in understanding the variability of functions. |
