New Approaches to Principal Component Analysis for Trees

Statistics in Biosciences

Volumn 4, Issue 1, 2012, Pages 132-156

  Aydın, Burcu ^a   Pataki, Gábor ^b   Wang, Haonan ^c   Ladha, Alim ^b   Bullitt, Elizabeth ^d   Marron, J S ^b  

^a HEWLETT PACKARD LABORATORIES   (United States)

^b UNIVERSITY OF NORTH CAROLINA   (United States)

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

^d UNIVERSITY OF NORTH CAROLINA SCHOOL OF MEDICINE   (United States)

Author keywords

Binary trees; Object oriented data analysis; Principal component analysis; Tree lines; Vessel structure

Indexed keywords

ALGORITHM; ANALYTIC METHOD; ARTICLE; BRAIN ARTERY; CLUSTER ANALYSIS; DATA ANALYSIS; DATA SYNTHESIS; LINEAR SYSTEM; MATHEMATICAL COMPUTING; PRINCIPAL COMPONENT ANALYSIS; PRIORITY JOURNAL; PROCESS DEVELOPMENT; PROCESS OPTIMIZATION; STATISTICAL ANALYSIS; STATISTICAL SIGNIFICANCE; STRUCTURE ANALYSIS;

EID: 84862790018     PISSN: 18671764     EISSN: 18671772     Source Type: Journal    
DOI: 10.1007/s12561-012-9055-8     Document Type: Article

References (22)

1. Alfaro CA, Aydin B, Bullitt E, Ladha A, Valencia CE (2011) Dimension reduction in principal component analysis for trees. Manuscript in progress.
2. Aydin B (2009) Principal component analysis of tree structured objects. Ph. D. Thesis, University of North Carolina at Chapel Hill.
3. Aydin B, Pataki G, Wang H, Bullitt E, Marron JS (2009) A principal component analysis for trees. Ann Appl Stat 3: 1597-1615.
4. Aydin B, Pataki G, Wang H, Ladha A, Bullitt E, Marron JS (2011) Visualizing the structure of large trees. Electron J Stat 5: 405-420.
5. Aylward S, Bullitt E (2002) Initialization, noise, singularities and scale in height ridge traversal for tubular object centerline extraction. IEEE Trans Med Imaging 21: 61-75.
6. Banks D, Constantine GM (1998) Metric models for random graphs. J Classif 15: 199-223.
7. Bazaraa MS, Shetty CM (1979) Nonlinear programming: Theory and algorithms. Wiley, New York.
8. Breiman L (1996) Bagging predictors. Mach Learn 24(2): 123-140.
9. Breiman L, Friedman JH, Olshen JA, Stone CJ (1984) Classification and regression trees. Wadsworth, Belmont.
10. Bullitt E, Gerig G, Pizer SM, Aylward SR (2003) Measuring tortuosity of the intracerebral vasculature from MRA images. IEEE Trans Med Imaging 22: 1163-1171.
11. Bullitt E, Zeng D, Ghosh A, Aylward SR, Lin W, Marks BL, Smith K (2010) The effects of healthy aging on intracerebral blood vessels visualized by magnetic resonance angiography. Neurobiol Aging 31(2): 290-300.
12. Cook WJ, Cunningham WH, Pulleyblank WR, Schrijver A (1997) Combinatorial optimization. Wiley, New York.
13. Everitt BS, Landau S, Leese M (2001) Cluster analysis, 4th edn. Oxford University Press, New York.
14. Handle, http://hdl. handle. net/1926/594 (2008).
15. Land AH, Doig AG (1960) An automatic method of solving discrete programming problems. Econometrica 28(3): 497-520.
16. Lawler EL, Bell MD (1966) A method for solving discrete optimization problems. Oper Res 14(6): 1098-1112.
17. Lawler EL, Wood DE (1966) Branch-and-bound methods: A survey. Oper Res 14: 699-719.
18. Nye T (2011) Principal component analysis in the space of phylogenetic trees. Unpublished manuscript, http://www. mas. ncl. ac. uk/~ntmwn/pca/preprint. pdf.
19. Schrijver A (1998) Theory of linear and integer programming. Wiley, New York.
20. Shen D, Shen H, Bhamidi S, Munoz-Maldonado Y, Kim Y, Marron JS (2011) Functional data analysis for trees. Manuscript in progress.
21. Wang H, Marron JS (2007) Object oriented data analysis: sets of trees. Ann Stat 35: 1849-1873.
22. Wang Y, Marron JS, Aydin B, Ladha A, Bullitt E, Wang H (2011) Nonparametric regression model with tree-structured response. Manuscript in progress.