A principal component analysis for trees

Annals of Applied Statistics

Volumn 3, Issue 4, 2009, Pages 1597-1615

  Aydin, Burcu ^a   Pataki, Gábor ^a   Wang, Haonan ^b   Bullitt, Elizabeth ^a   Marron, J S ^a  

^a UNIVERSITY OF NORTH CAROLINA   (United States)

^b Department of Environmental and Radiological Health Sciences   (United States)

Author keywords

Object oriented data analysis; Population structure; Principal component analysis; Tree lines; Tree structured objects

Indexed keywords

EID: 77952385728     PISSN: 19326157     EISSN: 19417330     Source Type: Journal    
DOI: 10.1214/09-AOAS263     Document Type: Article

References (18)

1. 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.
2. Banks, D. and Constantine, G. M. (1998). Metric models for random graphs. J. Classification 15 199-223.
3. Breiman, L. (1996). Bagging predictors. Mach. Learn. 24 123-140.
4. Breiman, L., Friedman, J. H., Olshen, J. A. and Stone, C. J. (1984). Classification and Regression Trees. Wadsworth, Belmont, CA.
5. Bullitt, E., Zeng, D., Ghosh, A., Aylward, S. R., Lin, W., Marks, B. L. and Smith, K. (2008). The effects of healthy aging on intracerebral blood vessels visualized by magnetic resonance angiography. Neurobiology of Aging. To appear.
6. Collins, M. and Duffy, N. (2002). Convolution kernels for natural language. In Advances in Neural Information Processing Systems 14 625-632. MIT Press, Cambridge, MA.
7. Eom, J.-H., Kim, S., Kim, S.-H. and Zhang, B.-T. (2006). A tree kernel-based method for protein-protein interaction mining from biomedical literature. In Knowledge Discovery in Life Science Literature, PAKDD 2006 International Workshop, Proceedings. Lecture Notes in Computer Science 3886. Springer, Singapore.
8. Everitt, B. S., Landau, S. and Leese, M. (2001). Cluster Analysis, 4th ed. Oxford Univ. Press, New York.
9. Ferraty, F. and Vieu, P. (2006). Nonparametric Functional Data Analysis: Theory and Practice. Springer, Berlin.
10. Holmes, S. (1999). Phylogenies: An overview. In Statistics and Genetics(Halloran and Geisser, eds.). IMA Volumes in Mathematics and Its Applications 112 81-119. Springer, New York.
11. Li, S., Pearl, D. K. and Doss, H. (2000). Phylogenetic tree constructure using Markov chain Monte Carlo. J. Amer. Statist. Assoc. 95 493-508.
12. Pachter, L. and Sturmfels, B. (2005). Algebraic Statistics for Computational Biology. Cambridge Univ. Press, Cambridge, UK.
13. Ramsay, J. O. and Silverman, B. W. (2002). Applied Functional Data Analysis. Springer, New York.
14. Ramsay, J. O. and Silverman, B. W. (2005). Functional Data Analysis, 2nd ed. Springer, New York.
15. Shawe-Taylor, J. and Cristianini, N. (2004). Kernel Methods for Pattern Analysis. Cambridge Univ. Press, New York.
16. Vert, J. P. (2002). A tree kernel to analyse phylogenetic profiles. Bioinformatics 18 Suppl. 1 276-284.
17. Wang, H. and Marron, J. S. (2007). Object oriented data analysis: Sets of trees. Ann. Statist. 35 1849-1873.
18. Yamanishi, Y., Bach, F. and Vert, J. P. (2007). Glycan classification with tree kernels. Bioinformatics 23 1211-1216.