2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170776The active field of Functional Data Analysis (about understanding the variation in a set of curves) has been recently extended to Object Oriented Data Analysis, which considers populations of more general objects. A particularly challenging extension of this set of ideas is to populations of tree-structured objects. We develop an analog of Principal Component Analysis for trees, based on the notion of tree-lines, and propose numerically fast (linear time) algorithms to solve the resulting optimization problems. The solutions we obtain are used in the analysis of a data set of 73 individuals, where each data object is a tree of blood vessels in one person's brain.Statistics TheoryOptimization and ControlQuantitative MethodsComputation62H99, 62G99, 05C05, 9008text