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Principal differential analysis of the Aneurisk65 data set

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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.

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Notes

  1. The project involved MOX Laboratory for Modeling and Scientific Computing (Dip. di Matematica, Politecnico di Milano), Laboratory of Biological Structure Mechanics (Dip. di Ingegneria Strutturale, Politecnico di Milano), Istituto Mario Negri (Ranica), Ospedale Niguarda Ca? Granda (Milano) and Ospedale Maggiore Policlinico (Milano), and has been supported by Fondazione Politecnico di Milano and Siemens Medical Solutions Italia. Detailed descriptions of the project’s aims can be found at AneuRisk webpage http://mox.polimi.it/it/progetti/aneurisk/, where AneuRisk65 data can be downloaded. These data include the image reconstructions of one of the main cerebral vessels, the Inner Carotid Artery (ICA), described in terms of the vessel centreline and of the vessel radius profile. An increasing data warehouse concerning aneurysm pathology can be accessed from the AneuRisk Web Repository http://ecm2.mathcs.emory.edu/aneurisk managed by Emory University and Orobix.

References

  • Antiga L, Piccinelli M, Botti L, Ene-Iordache B, Remuzzi A, Steinman DA (2008) An image-based modeling framework for patient-specific computational hemodynamics. Med Biol Eng Comput 46:1097–1120

    Article  Google Scholar 

  • Feynman R, Leighton R, Sands M (2013) The Feynman lectures on physics, vol 1, online edition. In: Gottlieb MA, Pfeiffer R (eds) http://www.feynmanlectures.caltech.edu. Basic Books

  • Passerini T, Sangalli LM, Vantini S, Piccinelli M, Bacigaluppi S, Antiga L, Boccardi E, Secchi P, Veneziani A (2012) An integrated CFD-statistical investigation of parent vasculature of cerebral aneurysms. Cardiol Eng Tech 3(1):26–40

    Article  Google Scholar 

  • Patriarca M, Sangalli LM, Secchi P, Vantini S, Vitelli V (2013) fdakma: Clustering and alignment of of a functional dataset. R package version 1.0. http://CRAN.R-project.org/package=fdakma

  • Poyton AA, Varziri MS, McAuley KB, McLellan P-J, Ramsay JO (2006) Parameter estimation in continuous-time dynamic models using principal differential analysis. Comput Chem Eng 30:698–708

    Article  Google Scholar 

  • R Core Team (2012) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org/

  • Ramsay JO (1996) Principal differential analysis: data reduction by differential operators. J R Stat Soc Ser B 58(3):495–508

    MATH  MathSciNet  Google Scholar 

  • Ramsay JO, Munhall KG, Gracco VL, Ostry DJ (1996) Functional data analysis of lip motion. J Acoust Soc Am 99:3718–3727

    Article  Google Scholar 

  • Ramsay JO (2000) Functional components of variation in handwrinting. J Am Stat Assoc 95:9–16

    Article  Google Scholar 

  • Ramsay JO, Silverman BW (2005) Functional data analysis, IInd edn. Springer, NY

    Google Scholar 

  • Reimer M, Rudzicz F (2010) Identifying articulatory goals from kinematic data using principal differential analysis. Proc Interspeech 2010:1608–1611

    Google Scholar 

  • Rudin W (1991) Functional analysis, 2nd edn. McGraw-Hill, New York

    MATH  Google Scholar 

  • Sangalli LM, Vantini S, Secchi P, Veneziani A (2009) A case study in exploratory functional data analysis: geometrical features of the internal carotid artery. J Am Stat Assoc 104(485):37–48

    Article  MathSciNet  Google Scholar 

  • Wang S, Jank W, Shmueli G, Smith P (2008) Modeling price dynamics in eBay auctions using differential equations. J Am Stat Assoc 103(483):1100–1118

    Article  MATH  MathSciNet  Google Scholar 

  • Winsberg S, Depalle P (1999) Applications of principal differential analysis to data reduction and extraction of musical features of sound. In: Proceedings of international computer music conference (ICMC’99)

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Authors and Affiliations

  1. MOX - Department of Mathematics, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 , Milano, Italy

    Matilde Dalla Rosa, Laura M. Sangalli & Simone Vantini

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  1. Matilde Dalla Rosa
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  2. Laura M. Sangalli
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  3. Simone Vantini
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Correspondence to Simone Vantini.

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Dalla Rosa, M., Sangalli, L.M. & Vantini, S. Principal differential analysis of the Aneurisk65 data set. Adv Data Anal Classif 8, 287–302 (2014). https://doi.org/10.1007/s11634-014-0175-5

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  • DOI: https://doi.org/10.1007/s11634-014-0175-5

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