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Principal differential analysis of the Aneurisk65 data set

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  • Matilde Dalla Rosa
  • Laura Sangalli
  • Simone Vantini

Abstract

We explore the use of principal differential analysis as a tool for performing dimensional reduction of functional data sets. In particular, we compare the results provided by principal differential analysis and by functional principal component analysis in the dimensional reduction of three synthetic data sets, and of a real data set concerning 65 three-dimensional cerebral geometries, the AneuRisk65 data set. The analyses show that principal differential analysis can provide an alternative and effective representation of functional data, easily interpretable in terms of exponential, sinusoidal, or damped-sinusoidal functions and providing a different insight to the functional data set under investigation. Moreover, in the analysis of the AneuRisk65 data set, principal differential analysis is able to detect interesting features of the data, such as the rippling effect of the vessel surface, that functional principal component analysis is not able to detect. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Matilde Dalla Rosa & Laura Sangalli & Simone Vantini, 2014. "Principal differential analysis of the Aneurisk65 data set," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(3), pages 287-302, September.
    • Handle: RePEc:spr:advdac:v:8:y:2014:i:3:p:287-302
    DOI: 10.1007/s11634-014-0175-5
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    References listed on IDEAS

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    1. Sangalli, Laura M. & Secchi, Piercesare & Vantini, Simone & Veneziani, Alessandro, 2009. "A Case Study in Exploratory Functional Data Analysis: Geometrical Features of the Internal Carotid Artery," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 37-48.
    2. Wang, Shanshan & Jank, Wolfgang & Shmueli, Galit & Smith, Paul, 2008. "Modeling Price Dynamics in eBay Auctions Using Differential Equations," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1100-1118.
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    1. Pini, Alessia & Spreafico, Lorenzo & Vantini, Simone & Vietti, Alessandro, 2019. "Multi-aspect local inference for functional data: Analysis of ultrasound tongue profiles," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 162-185.
    2. Pini, Alessia & Stamm, Aymeric & Vantini, Simone, 2018. "Hotelling’s T2 in separable Hilbert spaces," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 284-305.

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