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Local Correlation Integral Approach for Anomaly Detection Using Functional Data

Author

Listed:
  • Jorge R. Sosa Donoso

    (Department of Mathematics, Faculty of Sciences, Escuela Politécnica Nacional, Quito 170517, Ecuador)

  • Miguel Flores

    (MODES Group, Department of Mathematics, Faculty of Sciences, Escuela Politécnica Nacional, Quito 170517, Ecuador)

  • Salvador Naya

    (MODES Group, CITIC, Department of Mathematics, Escola Politécnica de Enxeñaría de Ferrol, Universidade da Coruña, 15403 Ferrol, Spain)

  • Javier Tarrío-Saavedra

    (MODES Group, CITIC, Department of Mathematics, Escola Politécnica de Enxeñaría de Ferrol, Universidade da Coruña, 15403 Ferrol, Spain)

Abstract

The present work develops a methodology for the detection of outliers in functional data, taking into account both their shape and magnitude. Specifically, the multivariate method of anomaly detection called Local Correlation Integral (LOCI) has been extended and adapted to be applied to the particular case of functional data, using the calculation of distances in Hilbert spaces. This methodology has been validated with a simulation study and its application to real data. The simulation study has taken into account scenarios with functional data or curves with different degrees of dependence, as is usual in cases of continuously monitored data versus time. The results of the simulation study show that the functional approach of the LOCI method performs well in scenarios with inter-curve dependence, especially when the outliers are due to the magnitude of the curves. These results are supported by applying the present procedure to the meteorological database of the Alternative Energy and Environment Group in Ecuador, specifically to the humidity curves, presenting better performance than other competitive methods.

Suggested Citation

  • Jorge R. Sosa Donoso & Miguel Flores & Salvador Naya & Javier Tarrío-Saavedra, 2023. "Local Correlation Integral Approach for Anomaly Detection Using Functional Data," Mathematics, MDPI, vol. 11(4), pages 1-18, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:815-:d:1058990
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    References listed on IDEAS

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    2. Ali, Asghar & Hussain, Rashida & Javed, Sara, 2024. "Exploring the dynamics of Lie symmetry, Bifurcation and Sensitivity analysis to the nonlinear Schrödinger model," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

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