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Outlier detection of clustered functional data with image and signal processing applications by archetype analysis

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  • Aleix Alcacer
  • Irene Epifanio

Abstract

In this study, we introduce an innovative methodology for anomaly detection of curves, applicable to both multivariate and multi-argument functions. This approach distinguishes itself from prior methods by its capability to identify outliers within clustered functional data sets. We achieve this by extending the recent AA + kNN technique, originally designed for multivariate analysis, to functional data contexts. Our method demonstrates superior performance through a comprehensive comparative analysis against twelve state-of-the-art techniques, encompassing simulated scenarios with either a single functional cluster or multiple clusters. Additionally, we substantiate the effectiveness of our approach through its application in three distinct computer vision tasks and a signal processing problem. To facilitate transparency and replication of our results, we provide access to both the code and the datasets used in this research.

Suggested Citation

  • Aleix Alcacer & Irene Epifanio, 2024. "Outlier detection of clustered functional data with image and signal processing applications by archetype analysis," PLOS ONE, Public Library of Science, vol. 19(11), pages 1-23, November.
    • Handle: RePEc:plo:pone00:0311418
    DOI: 10.1371/journal.pone.0311418
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    References listed on IDEAS

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    1. Irene Epifanio & M. Victoria Ibáñez & Amelia Simó, 2020. "Archetypal Analysis With Missing Data: See All Samples by Looking at a Few Based on Extreme Profiles," The American Statistician, Taylor & Francis Journals, vol. 74(2), pages 169-183, April.
    2. Manuel Febrero & Pedro Galeano & Wenceslao González-Manteiga, 2007. "A functional analysis of NOx levels: location and scale estimation and outlier detection," Computational Statistics, Springer, vol. 22(3), pages 411-427, September.
    3. Pierpaolo D’Urso & Livia Giovanni & Riccardo Massari, 2021. "Trimmed fuzzy clustering of financial time series based on dynamic time warping," Annals of Operations Research, Springer, vol. 299(1), pages 1379-1395, April.
    4. Jacques, Julien & Preda, Cristian, 2014. "Model-based clustering for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 92-106.
    5. Epifanio, Irene, 2016. "Functional archetype and archetypoid analysis," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 24-34.
    6. Dai, Wenlin & Genton, Marc G., 2019. "Directional outlyingness for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 50-65.
    7. Cuesta-Albertos, Juan Antonio & Fraiman, Ricardo, 2007. "Impartial trimmed k-means for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4864-4877, June.
    8. Ferrando, L. & Epifanio, I. & Ventura-Campos, N., 2021. "Ordinal classification of 3D brain structures by functional data analysis," Statistics & Probability Letters, Elsevier, vol. 179(C).
    9. Irene Epifanio & Vicent Gimeno & Ximo Gual-Arnau & M. Victoria Ibáñez-Gual, 2020. "A New Geometric Metric in the Shape and Size Space of Curves in R n," Mathematics, MDPI, vol. 8(10), pages 1-19, October.
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