Electronic Journal of Statistics

Analysis of AneuRisk65 data: $k$-mean alignment

Laura M. Sangalli, Piercesare Secchi, and Simone Vantini

Full-text: Open access

Abstract

We describe the $k$-mean alignment procedure, for the joint alignment and clustering of functional data and we apply it to the analysis of the AneuRisk65 data. Thanks to the efficient separation of the variability in phase variability and within/between clusters amplitude variability, we are able to discriminate subjects having aneurysms in different cerebral districts and identifying different morphological shapes of Inner Carotid Arteries, unveiling a strong association between arteries morphologies and the aneurysmal pathology.

Article information

Source
Electron. J. Statist., Volume 8, Number 2 (2014), 1891-1904.

Dates
First available in Project Euclid: 29 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1414588177

Digital Object Identifier
doi:10.1214/14-EJS938A

Mathematical Reviews number (MathSciNet)
MR3273609

Zentralblatt MATH identifier
1305.62377

Keywords
$k$-mean alignment registration functional clustering AneuRisk65 data

Citation

Sangalli, Laura M.; Secchi, Piercesare; Vantini, Simone. Analysis of AneuRisk65 data: $k$-mean alignment. Electron. J. Statist. 8 (2014), no. 2, 1891--1904. doi:10.1214/14-EJS938A. https://projecteuclid.org/euclid.ejs/1414588177


Export citation

References

  • Bernardi, M., Sangalli, L. M., Secchi, P. and Vantini, S. (2014a). Analysis of proteomics data: Block $k$-mean alignment., Electronic Journal of Statistics 8 1714–1723, Special Section on Statistics of Time Warpings and Phase Variations.
  • Bernardi, M., Sangalli, L. M., Secchi, P. and Vantini, S. (2014b). Analysis of juggling data: An application of $k$-mean alignment., Electronic Journal of Statistics 8 1817–1824, Special Section on Statistics of Time Warpings and Phase Variations.
  • Ferraty, F. and Vieu, P. (2006)., Nonparametric Functional Data Analysis. Springer.
  • Kneip, A. and Gasser, T. (1988). Convergence and consistency results for self-modeling nonlinear regression., The Annals of Statistics 16 82–112.
  • Krayenbuehl, H., Huber, P. and Yasargil, M. G. (1982). Krayenbuhl/Yasargil Cerebral Angiography., Thieme Medical Publishers, 2nd ed.
  • Lawton, W. H., Sylvestre, E. A. and Maggio, M. S. (1972). Self modeling nonlinear regression., Technometrics 14 513–532.
  • Parodi, A., Patriarca, M., Sangalli, L., Secchi, P., Vantini, S. and Vitelli, V. (2014). fdakma: Clustering and alignment of a functional dataset, R package version, 1.1.
  • Passerini, T., Sangalli, L. M., Vantini, S., Piccinelli, M., Bacigaluppi, S., Antiga, L., Boccardi, E., Secchi, P. and Veneziani, A. (2012). An integrated CFD-statistical investigation of parent vasculature of cerebral aneurysms., Cardio. Eng. and Tech. 3 26–40.
  • Patriarca, M., Sangalli, L. M., Secchi, P. and Vantini, S. (2014). Analysis of spike train data: An application of $k$-mean alignment., Electronic Journal of Statistics 8 1769–1775, Special Section on Statistics of Time Warpings and Phase Variations.
  • Ramsay, J. O. and Silverman, B. W. (2005)., Functional data analysis, second ed. Springer Series in Statistics. Springer, New York.
  • Sangalli, L. M., Secchi, P. and Vantini, S. (2013). AneuRisk65: A dataset of three-dimensional cerebral vascular geometries., Electronic Journal of Statistics 8 1879–1890, Special Section on Statistics of Time Warpings and Phase Variations.
  • Sangalli, L. M., Secchi, P., Vantini, S. and Veneziani, A. (2009). A case study in exploratory functional data analysis: Geometrical Features of the Internal Carotid Artery., J. Amer. Statist. Assoc. 104 37–48.
  • Sangalli, L. M., Secchi, P., Vantini, S. and Vitelli, V. (2010). K-mean alignment for curve clustering., Computational Statistics and Data Analysis 54 1219–1233.
  • Tarpey, T. and Kinateder, K. K. J. (2003). Clustering functional data., Journal of Classification 20 93–114.
  • Vantini, S. (2012). On the definition of phase and amplitude variability in functional data analysis., TEST 21 676–696.
  • Wu, W. and Srivastava, A. (2014). Analysis of spike train data: Alignment and comparisons using extended Fisher-Rao metric., Electronic Journal of Statistics 8 1776–1785, Special Section on Statistics of Time Warpings and Phase Variations.

See also

  • Related item: Sangalli, L. M., Secchi, P., Vantini, S. (2014). AneuRisk65: A dataset of three-dimensional cerebral vascular geometries. Electron. J. Statist. 8 1879–1890.