Functional data analysis of tree data objects

Journal of Computational and Graphical Statistics

Volumn 23, Issue 2, 2014, Pages 418-438

  Shen, Dan ^a   Shen, Haipeng ^a   Bhamidi, Shankar ^a   Muñoz Maldonado, Yolanda ^b   Kim, Yongdai ^c   Marron, J S ^a  

^a University of North Carolina at Chapel Hill   (United States)

^b WILLIAM BEAUMONT HOSPITAL   (United States)

^c Seoul National University   (South Korea)

Author keywords

Branch length; DiProPerm; Dyck path; Support tree; Tree pruning

Indexed keywords

EID: 84901793170     PISSN: 10618600     EISSN: 15372715     Source Type: Journal    
DOI: 10.1080/10618600.2013.786943     Document Type: Article

References (33)

1. Aydin, B., Pataki, G., Wang, H., Bullitt, E., and Marron, J. (2009), "A Principal Component Analysis for Trees, " The Annals of Applied Statistics, 3, 1597-1615. [419,420]
2. Aydin, B., Pataki, G., Wang, H., Ladha, A., Bullitt, E., and Marron, J. (2011), "Visualizing the Structure of Large Trees, " Electronic Journal of Statistics, 5, 405-420. [419]
3. Aydin, B., Pataki, G., Wang, H., Ladha, A., Bullitt, E., and Marron, J. (2012), "New Approaches to Principal Component Analysis for Trees, " Statistics in Biosciences, 4, 132-156. [419]
4. Aylward, S., and Bullitt, E. (2002), "Initialization, Noise, Singularities, and Scale in Height Ridge Traversal for Tubular Object Centerline Extraction, " IEEE Transactions on Medical Imaging, 21, 61-75. [419]
5. Benjamini, Y., and Yekutieli, D. (2001), "The Control of the False Discovery Rate in Multiple Testing Under Dependency, " The Annals of Statistics, 29, 1165-1188. [433]
6. Billera, L., Holmes, S., and Vogtmann, K. (2001), "Geometry of the Space of Phylogenetic Trees, " Advances in Applied Mathematics, 27, 733-767. [419,437]
7. Collins, M., and Duffy, N. (2001), "Convolution Kernels for Natural Language, " in Proceedings of NIPS (Vol. 14), pp. 625-632. [419]
8. Dryden, I., and Mardia, K. (1998), Statistical Shape Analysis (Vol. 4), New York: Wiley. [420]
9. Dumoulin, C., and Hart, H. (1986), "Magnetic Resonance Angiography, " Radiology, 161, 717-720. [420]
10. Eom, J., Kim, S., Kim, S., and Zhang, B. (2006), "A Tree Kernel-Based Method for Protein-Protein Interaction Mining From Biomedical Literature, " Knowledge Discovery in Life Science Literature, 3886, 42-52. [419]
11. Feragen, A., Lauze, F., Lo, P., de Bruijne, M., and Nielsen, M. (2010), "Geometries on Spaces of Treelike Shapes, " in Proceedings of the 10th Asian Conference on Computer Vision-Volume Part II, pp. 160-173. [420,437]
12. Ferraty, F., and Vieu, P. (2006), Nonparametric Functional Data Analysis: Theory and Practice, New York: Springer Verlag. [418]
13. Handle (2008), Tree Data, available at http://hdl.handle.net/1926/594. [420]
14. Hannig, J., and Marron, J. (2006), "Advanced Distribution Theory for Sizer, " Journal of the American Statistical Association, 101, 484-499. [428]
15. Härdle, W., and Simar, L. (2007), Applied Multivariate Statistical Analysis, New York: Springer Verlag. [431]
16. Harris, T. (1952), "First Passage and Recurrence Distributions, " Transactions of the American Mathematical Society, 73, 471-486. [419]
17. Jolliffe, I. (2002), Principal Component Analysis, New York: Springer Verlag. [419]
18. Kim, Y., and Lee, J. (2003), "Bayesian Bootstrap for Proportional Hazards Models, " The Annals of Statistics, 31, 1905-1922. [437]
19. Lee, D., and Seung, H. (2001), "Algorithms for Non-Negative Matrix Factorization, " Advances in Neural Information Processing Systems, 13, 556-562. [428]
20. Marron, J., Todd, M., and Ahn, J. (2007), "Distance-Weighted Discrimination, " Journal of the American Statistical Association, 102, 1267-1271. [430]
21. Qiao, X., Zhang, H., Liu, Y., Todd, M., and Marron, J. (2010), "Weighted Distance Weighted Discrimination and Its Asymptotic Properties, " Journal of the American Statistical Association, 105, 401-414. [430]
22. Ramsay, J., and Silverman, B. (2002), Applied Functional Data Analysis: Methods and Case Studies, New York: Springer Verlag. [418,424]
23. Ramsay, J., and Silverman, B. (2005), Functional Data Analysis, New York: Springer Verlag. [418,424]
24. Shawe-Taylor, J., and Cristianini, N. (2004), Kernel Methods for Pattern Analysis, Cambridge: Cambridge University Press. [419]
25. Shen, D. (2012), Sparse PCA Asymptotics and Analysis of Tree Data, Ph. d Thesis, Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, North Carolina. [431,433,434,435,436]
26. Shen, D., Shen, H., and Marron, J. S. (2013), "Consistency of Sparse PCA in High Dimension, Low Sample Size Contexts, " Journal of Multivariate Analysis, 115, 317-333. [426]
27. Vert, J. (2002), "A Tree Kernel to Analyse Phylogenetic Profiles, " Bioinformatics, 18, 276-284. [419]
28. Wang, H., and Marron, J. (2007), "Object Oriented Data Analysis: Sets of Trees, " The Annals of Statistics, 35, 1849-1873. [418]
29. Wei, S., Lee, C., Wichers, L., Li, G., and Marron, J. (2012), "Direction-Projection-Permutation for High Dimensional Hypothesis Tests, " Technical Report, Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, North Carolina. [430]
30. Wichers, L., Lee, C., Costa, D., Watkinson, W., and Marron, J. (2007), "A Functional Data Analysis Approach for Evaluation Temporal Physiologic Responses to Particulate Matter, " Technical Report 5, Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, North Carolina. [430]
31. Wold, S., Ruhe, A., Wold, H., and Dunn III, W. (1984), "The Collinearity Problem in Linear Regression. The Partial Least Squares (PLS) Approach to Generalized Inverses, " SIAM Journal on Scientific and Statistical Computing, 5, 735-743. [431]
32. Yamanishi, Y., Bach, F., and Vert, J. (2007), "Glycan Classification With Tree Kernels, " Bioinformatics, 23, 1211-1216. [419]
33. Yao, F., Müller, H., Clifford, A., Dueker, S., Follett, J., Lin, Y., Buchholz, B., and Vogel, J. (2003), "Shrinkage Estimation for Functional Principal Component ScoresWith Application to the Population Kinetics of Plasma Folate, " Biometrics, 59, 676-685. [424]