Statistical Analysis on Tree-Structured Objects

Sienkiewicz, E. and Wang, H. (2018). Pareto Quantiles of Unlabeled Tree Objects. The Annals of Statistics, 46, 1513-1540.

Chang, H.-W., Iyer, H., Bullitt, E. and Wang, H. (2013). Generalized Linear Mixed Models for Branching Probabilities of Brain Artery Systems. Model Assisted Statistics and Applications, 8, 121-133.

Wang, Y., Marron, J.S., Aydin, Ladha, A., Bullitt, E. and Wang, H. (2012). A Nonparametric Regression Model with Tree-structured Response. Journal of the American Statistical Association, 107, 1272-1285.

Aydin, B., Pataki, G., Wang, H., Ladha, A., Bullitt, E. and Marron, J.S. (2012). New Approaches to Principal Component Analysis. Statistics in Biosciences, 4, 132-156.

Aydin, B., Pataki, G., Wang, H., Ladha, A., Bullitt, E. and Marron, J.S. (2011). Visualizing the Structure of Large Trees. Electronic Journal of Statistics, 5, 405-420.

Aydin, B., Pataki, G., Wang, H. , Bullitt, E. and Marron, J.S. (2009). A Principal Component Analysis for Trees. The Annals of Applied Statistics, 3, 1597-1615.

Wang, H. and Marron, J. S. (2007). Object Oriented Data Analysis: Sets of Trees. The Annals of Statistics, 35, 1849-1873

 

Supplemental Material

Generalized Linear Mixed Models for Branching Probabilities of Brain Artery Systems.

A draft of the paper can be downloaded Here.

A Nonparametric Regression Model with Tree-structured Response.

A draft of the paper can be downloaded Here. The supplemental material can be downloaded Here.

Here are some supplemental movies for the simulation study in this paper:

• Scenario 1
• Scenario 2
• Scenario 3
• Scenario 4

Visualizing the Structure of Large Trees.

A draft of the paper can be downloaded Here or arXiv.

A Principal Component Analysis for Trees.

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:
  1. Scatterplots of scores belonging to principal components 1, 2, 3 and 4: Back, Left and Right
  2. Scatterplots of *cumulative* scores belonging to principal components 1, 2, 3 and 4: Back, Left and Right
  3. Scatterplots of age parameter with principal components 1, 2 and 3: Back, Left and Right
     

• Descendant Correspondence:
  1. Scatterplots of scores belonging to principal components 1, 2, 3 and 4: Back, Left and Right
  2. Scatterplots of *cumulative* scores belonging to principal components 1, 2, 3 and 4: Back, Left and Right
  3. Scatterplots of age parameter with principal components 1, 2 and 3: Back, Left and Right
     

Object Oriented Data Analysis: Sets of Trees.

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: first person second person and third person
• 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:

• Wang, H. and Marron, J.S. (2005) pdf