Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tree Oriented Data Analysis   Complex data objects arise in many areas of modern science including
evolutionary biology, nueroscience, dynamics of gene expression and medical
imaging. Object oriented data analysis (OODA) is the statistical analysis of
datasets of complex objects. Data analysis of tree data objects is an exciting
research area with interesting questions and challenging problems. This thesis
focuses on tree oriented statistical methodologies, and algorithms for solving
related mathematical optimization problems.
  This research is motivated by the goal of analyzing a data set of images of
human brain arteries. The approach we take here is to use a novel
representation of brain artery systems as points in phylogenetic treespace. The
treespace property of unique global geodesics leads to a notion of geometric
center called a Fr\'echet mean. For a sample of data points, the Fr\'echet
function is the sum of squared distances from a point to the data points, and
the Fr\'echet mean is the minimizer of the Fr\'echet function.
  In this thesis we use properties of the Fr\'echet function to develop an
algorithmic system for computing Fr\'echet means. Properties of the Fr\'echet
function are also used to show a sticky law of large numbers which describes a
surprising stability of the topological tree structure of sample Fr\'echet
means at that of the population Fr\'echet mean. We also introduce
non-parametric regression of brain artery tree structure as a response variable
to age based on weighted Fr\'echet means.

6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
19
The categories of this paper are: eess
2
The categories of this paper are: math
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics