Statistical Analysis on Tree-structured objects:
1. Object Oriented Data Analysis: Sets of
Trees. (with J.
S. Marron)
Here are some movies for this paper: (It may
take around 30 seconds to load one movie)
·
3D view of the
individual simplified blood vessel trees:
·
3D view of the
sample of simplified blood vessel trees: sample
·
The attribute
treeline passing through the median-mean tree
·
The attribute treeline
passing through the average support tree
The complete draft of the paper with detail
proofs:
2. A Principal Component Analysis for Trees.
(with B. Aydin, G. Pataki, E. Bullitt and J. S. Marron )
A draft of the paper: arXiv
Here are some supplemental figures for this
paper:
·
The support trees
of 3 sub-populations for two correspondences: ST
·
For descendant
correspondence, the first three principal components for three sub-populations:
Lines
·
For left
sub-population, comparison of # of nodes explained with descendant and
thickness correspondences: Left Comparison
The paper includes a comparison of thickness
and descendant correspondence for back, left and right sub-populations:
Thickness Correspondence:
o
Scatterplots of
scores belonging to principal components 1, 2, 3 and 4:
o
Scatterplots of
*cumulative* scores belonging to principal components 1, 2, 3 and 4:
Descendant Correspondence:
o
Scatterplots of scores
belonging to principal components 1,2,3 and 4:
o
Scatterplots of
*cumulative* scores belonging to principal components 1, 2, 3 and 4:
o
Scatterplots of
age parameter with principal components 1, 2 and 3:
