Statistical Analysis on Tree-Structured Objects
Sienkiewicz, E. and Wang, H. (2017). Pareto Quantiles of Unlabeled Tree Objects. Accepted by the Annals of Statistics.
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. Accepted by 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
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.
Here are some supplemental movies for the simulation study in this paper:
Visualizing the Structure of Large Trees.
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:
- Descendant Correspondence:
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
B.S., Nankai University, Tianjin, China
Ph.D., University of North Carolina, Chapel Hill
Object Oriented Data Analysis
Statistical Analysis on Networks
216 Statistics Building
Department of Statistics
Colorado State University
Fort Collins, CO80523
My research has been supported by NSF grants DMS-0706761, DMS-0854903, DMS-1106975, DMS-1521746 and DMS-1737795 as well as grants with other collaborators.