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Functional outlier detection and taxonomy by sequential transformations

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  • Dai, Wenlin
  • Mrkvička, Tomáš
  • Sun, Ying
  • Genton, Marc G.

Abstract

Functional data analysis can be seriously impaired by abnormal observations, which can be classified as either magnitude or shape outliers based on their way of deviating from the bulk of data. Identifying magnitude outliers is relatively easy, while detecting shape outliers is much more challenging. We propose turning the shape outliers into magnitude outliers through data transformation and detecting them using the functional boxplot. Besides easing the detection procedure, applying several transformations sequentially provides a reasonable taxonomy for the flagged outliers. A joint functional ranking, which consists of several transformations, is also defined here. Simulation studies are carried out to evaluate the performance of the proposed method using different functional depth notions. Interesting results are obtained in several practical applications.

Suggested Citation

  • Dai, Wenlin & Mrkvička, Tomáš & Sun, Ying & Genton, Marc G., 2020. "Functional outlier detection and taxonomy by sequential transformations," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).
    • Handle: RePEc:eee:csdana:v:149:y:2020:i:c:s0167947320300517
    DOI: 10.1016/j.csda.2020.106960
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    References listed on IDEAS

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    1. Mari Myllymäki & Tomáš Mrkvička & Pavel Grabarnik & Henri Seijo & Ute Hahn, 2017. "Global envelope tests for spatial processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 381-404, March.
    2. Wenceslao González‐Manteiga & Rosa M. Crujeiras & Ying Sun & Marc G. Genton, 2012. "Adjusted functional boxplots for spatio‐temporal data visualization and outlier detection," Environmetrics, John Wiley & Sons, Ltd., vol. 23(1), pages 54-64, February.
    3. Febrero-Bande, Manuel & de la Fuente, Manuel Oviedo, 2012. "Statistical Computing in Functional Data Analysis: The R Package fda.usc," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i04).
    4. Kuhnt, Sonja & Rehage, André, 2016. "An angle-based multivariate functional pseudo-depth for shape outlier detection," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 325-340.
    5. Gerda Claeskens & Mia Hubert & Leen Slaets & Kaveh Vakili, 2014. "Multivariate Functional Halfspace Depth," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 411-423, March.
    6. Mia Hubert & Peter Rousseeuw & Pieter Segaert, 2015. "Multivariate functional outlier detection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 177-202, July.
    7. Anirvan Chakraborty & Probal Chaudhuri, 2014. "On data depth in infinite dimensional spaces," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 303-324, April.
    8. López-Pintado, Sara & Romo, Juan, 2009. "On the Concept of Depth for Functional Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 718-734.
    9. Weiyi Xie & Sebastian Kurtek & Karthik Bharath & Ying Sun, 2017. "A Geometric Approach to Visualization of Variability in Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 979-993, July.
    10. Naveen N. Narisetty & Vijayan N. Nair, 2016. "Extremal Depth for Functional Data and Applications," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1705-1714, October.
    11. Mia Hubert & Peter Rousseeuw & Pieter Segaert, 2015. "Rejoinder to ‘multivariate functional outlier detection’," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 269-277, July.
    12. Dai, Wenlin & Genton, Marc G., 2019. "Directional outlyingness for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 50-65.
    13. Ricardo Fraiman & Graciela Muniz, 2001. "Trimmed means for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 419-440, December.
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    Cited by:

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    3. Cristian Preda & Quentin Grimonprez & Vincent Vandewalle, 2021. "Categorical Functional Data Analysis. The cfda R Package," Mathematics, MDPI, vol. 9(23), pages 1-31, November.
    4. Ojo, Oluwasegun Taiwo & Fernández Anta, Antonio & Genton, Marc G., 2022. "Multivariate Functional Outlier Detection using the FastMUOD Indices," DES - Working Papers. Statistics and Econometrics. WS 35665, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Thomas-Agnan, Christine & Mondon, Camille & Trinh, Thi-Huong & Ruiz-Gazen, Anne, 2024. "ICS for complex data with application to outlier detection for density data objects," TSE Working Papers 24_1585, Toulouse School of Economics (TSE).
    6. Archimbaud, Aurore & Boulfani, Fériel & Gendre, Xavier & Nordhausen, Klaus & Ruiz-Gazen, Anne & Virta, Joni, 2021. "ICS for multivariate functional anomaly detection with applications to predictive maintenance and quality control," TSE Working Papers 21-1182, Toulouse School of Economics (TSE), revised Mar 2022.
    7. Helander, Sami & Laketa, Petra & Ilmonen, Pauliina & Nagy, Stanislav & Van Bever, Germain & Viitasaari, Lauri, 2022. "Integrated shape-sensitive functional metrics," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

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