814
Views
14
CrossRef citations to date
0
Altmetric
Original Articles

Functional Data Analysis of Tree Data Objects

Pages 418-438 | Received 01 Jul 2012, Published online: 28 Apr 2014

References

  • 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.
  • 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.
  • ——— (2012), “New Approaches to Principal Component Analysis for Trees,” Statistics in Biosciences, 4, 132–156.
  • 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.
  • 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.
  • Billera, L., Holmes, S., and Vogtmann, K. (2001), “Geometry of the Space of Phylogenetic Trees,” Advances in Applied Mathematics, 27, 733–767.
  • Collins, M., and Duffy, N. (2001), “Convolution Kernels for Natural Language,” in Proceedings of NIPS (Vol. 14), pp. 625–632.
  • Dryden, I., and Mardia, K. (1998), Statistical Shape Analysis (Vol. 4), New York: Wiley.
  • Dumoulin, C., and Hart, H. (1986), “Magnetic Resonance Angiography,” Radiology, 161, 717–720.
  • 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.
  • 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.
  • Ferraty, F., and Vieu, P. (2006), Nonparametric Functional Data Analysis: Theory and Practice, New York: Springer Verlag.
  • Handle (2008), Tree Data, available at http://hdl.handle.net/1926/594.
  • Hannig, J., and Marron, J. (2006), “Advanced Distribution Theory for Sizer,” Journal of the American Statistical Association, 101, 484–499.
  • Härdle, W., and Simar, L. (2007), Applied Multivariate Statistical Analysis, New York: Springer Verlag.
  • Harris, T. (1952), “First Passage and Recurrence Distributions,” Transactions of the American Mathematical Society, 73, 471–486.
  • Jolliffe, I. (2002), Principal Component Analysis, New York: Springer Verlag.
  • Kim, Y., and Lee, J. (2003), “Bayesian Bootstrap for Proportional Hazards Models,” The Annals of Statistics, 31, 1905–1922.
  • Lee, D., and Seung, H. (2001), “Algorithms for Non-Negative Matrix Factorization,” Advances in Neural Information Processing Systems, 13, 556–562.
  • Marron, J., Todd, M., and Ahn, J. (2007), “Distance-Weighted Discrimination,” Journal of the American Statistical Association, 102, 1267–1271.
  • 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.
  • Ramsay, J., and Silverman, B. (2002), Applied Functional Data Analysis: Methods and Case Studies, New York: Springer Verlag.
  • Ramsay, J., and Silverman, B. (2005), Functional Data Analysis, New York: Springer Verlag.
  • Shawe-Taylor, J., and Cristianini, N. (2004), Kernel Methods for Pattern Analysis, Cambridge: Cambridge University Press.
  • 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.
  • 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.
  • Vert, J. (2002), “A Tree Kernel to Analyse Phylogenetic Profiles,” Bioinformatics, 18, 276–284.
  • Wang, H., and Marron, J. (2007), “Object Oriented Data Analysis: Sets of Trees,” The Annals of Statistics, 35, 1849–1873.
  • 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.
  • 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.
  • 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.
  • Yamanishi, Y., Bach, F., and Vert, J. (2007), “Glycan Classification With Tree Kernels,” Bioinformatics, 23, 1211–1216.
  • Yao, F., Müller, H., Clifford, A., Dueker, S., Follett, J., Lin, Y., Buchholz, B., and Vogel, J. (2003), “Shrinkage Estimation for Functional Principal Component Scores With Application to the Population Kinetics of Plasma Folate,” Biometrics, 59, 676–685.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.