Abstract
This paper aims at discussing the interesting paper of Hubert et al. (Stat Methods Appl Appear, 2015), where a taxonomy of functional outliers and both numerical and graphical techniques for outlier detection for multivariate functional data are proposed. The reading has been really pleasant and instructive. We contribute to the discussion of the paper by Hubert et al. (2015), by discussing some points related to the extension of depth measures to the multivariate functional framework, by examining the fine line between outlier detection and classification and finally by pointing out some relevant open problems.
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References
Arribas-gIL A, Romo J (2014) Shape outlier detection and visualization for functional data: the outliergram. Biostatistics 15(4):603–619
Bache K, Lichman M (2013) UCI machine learning repository. http://archive.ics.uci.edu/ml
Brys G, Hubert M, Rousseeuw PJ (2005) A robustification of independent component analysis. J Chemom 19(5–7):364–375
Chenouri S, Liang J, Small CG (2015) Robust dimension reduction. WIREs Comput Stat 7:63–69
Claeskens G, Hubert M, Slaets L, Vakili K (2014) Multivariate functional halfspace depth. J Am Stat Assoc 109(505):411–423
Dyrby M, Engelsen S, Nørgaard L, Bruhn M, Lundsberg-Nielsen L (2002) Chemometric quantitation of the active substance in a pharmaceutical tablet using nearinfrared (nir) transmittance and nir ft-raman spectra. Appl Spectrosc 56(5):579–585
Hodge V, Austin J (2004) A survey of outlier detection methodologies. Artif Intell Rev 22(2):85–126
Hubert M, Rousseeuw P, Segaert P (2015) Multivariate functional outlier detection. Stat Methods Appl Appear. doi:10.1007/s10260-015-0297-8
Ieva F, Paganoni A (2013a) Depth measures for multivariate functional data. Commun Stat Theory Methods 42(7):1265–1276
Ieva F, Paganoni A (2013b) Risk prediction for myocardial infarction via generalized functional regression models. Stat Methods Med Res. doi:10.1177/0962280213495988
Ieva F, Paganoni A, Pigoli D, Vitelli V (2013) Multivariate functional clustering for the morphological analysis of ecg curves. J R Stat Soc Ser C (Appl Stat) 62(3):401–418
Kneip A, Li X, MacGibbon KB, Ramsay JO (2000) Curve registration by local regression. Can J Stat 28:19–29
Larsen F, van den Berg F, Engelsen S (2006) An exploratory chemometric study of nmr spectra of table wines. J Chemom 20(5):198–208
Lopez-Pintado S, Romo J (2007) Depth-based inference for functional data. Comput Stat Data Anal 51(10):4957–4968
Lopez-Pintado S, Romo J (2009) On the concept of depth for functional data. J Am Stat Assoc 104(486):718–734
Lopez-Pintado S, Sun Y, Genton M (2014) Simplicial band depth for multivariate functional data. Adv Data Anal Classif 8:321–338
Marron JS, Ramsay JO, Sangalli LM, Srivastava A (2014) Statistics of time warpings and phase variations. Electron J Stat 8(2):1697–1702
Ramsay JO, Li X (1998) Curve registration. J R Stat Soc Ser B 60:351–363
Ramsay JO, Silverman B (2005) Functional data analysis, 2nd edn. Springer, New York
Ritter G (2014) Robust cluster analysis and variable selection, 1st edn. CRC Press, Boca Raton
Rousseeuw P, Leroy A (2003) Robust regression and outlier detection, 3rd edn. Wiley, New York
Tarabelloni N, Ieva F, Biasi R, Paganoni AM (2013) Use of depth measure for multivariate functional data in disease prediction: an application to electrocardiographic signals. Tech. Rep. 54/2013, MOX - Dipartimento di Matematica, Politecnico di Milano. https://mox.polimi.it/publication
Vantini S (2012) On the definition of phase and amplitude variability in functional data analysis. Test 21:676–696
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Ieva, F., Paganoni, A.M. Discussion of “multivariate functional outlier detection” by M. Hubert, P. Rousseeuw and P. Segaert. Stat Methods Appl 24, 217–221 (2015). https://doi.org/10.1007/s10260-015-0303-1
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DOI: https://doi.org/10.1007/s10260-015-0303-1