<div class="csl-bib-body">
<div class="csl-entry">Mayrhofer, M., Radojičić, U., & Filzmoser, P. (2024, July 31). <i>Robust PCA and explainable outlier detection for multivariate functional data based on a functional Mahalanobis distance</i> [Conference Presentation]. ICORS meets DSSV 2024, United States of America (the). http://hdl.handle.net/20.500.12708/210706</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/210706
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dc.description.abstract
Outlier detection in multivariate functional data poses significant challenges due to the complex and high-dimensional nature of the data. In this study, we propose a new approach for explainable outlier detection utilizing Shapely values in conjunction with a truncated functional Mahalanobis semi-distance introduced in Galeano et al. [2015], thus focusing on capturing meaningful deviations while mitigating the influence of noise and irrelevant variations in the data.
Calculating truncated functional Mahalanobis distance involves the estimation of the covariance, which can be very biased in the presence of outliers in the data. To ensure robustness, we incorporate an adaptation of the matrix minimum determinant estimator (MMCD) introduced in Mayrhofer et al. [2024] for matrix-variate data, to robustly estimate the functional covariance, and demonstrate the validity of the procedure for the multivariate Gaussian processes. Additionally, robust covariance estimation leads to a robust functional principal component analysis.
Finally, Shapely values are employed to decompose the truncated Mahalanobis distance into contributions of individual features of the detected outliers, offering interpretability in the detection process, where the feature type depends on how we express the functional data object.
The effectiveness and interpretability of the proposed method are demonstrated in both simulated and real-data scenarios. In particular, the approach is applied to fertility curves calculated for various countries, where it was revealed that one can crudely group the studied countries based on when a sudden drop in fertility was observed. The results generally showcase the method’s ability to identify outliers in multivariate functional data while providing valuable insights into the underlying patterns contributing to anomalous observations.
en
dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.language.iso
en
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dc.subject
Mmcd
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dc.subject
Fda
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dc.subject
Pca
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dc.subject
Shapely Values
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dc.subject
Outlier Detection
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dc.title
Robust PCA and explainable outlier detection for multivariate functional data based on a functional Mahalanobis distance
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dc.type
Presentation
en
dc.type
Vortrag
de
dc.relation.grantno
I 5799-N
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dc.type.category
Conference Presentation
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tuw.publication.invited
invited
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tuw.project.title
Generalisierte relative Daten und Robustheit in Bayes Räumen
