<div class="csl-bib-body">
<div class="csl-entry">Puchhammer, P., & Filzmoser, P. (2023, June 12). <i>Detecting Local Outliers Using the Spatially Smoothed MRCD Estimator</i> [Conference Presentation]. Olomoucian Days of Applied Mathematics ODAM 2023, Olomouc, Czechia.</div>
</div>
-
dc.identifier.uri
http://hdl.handle.net/20.500.12708/200067
-
dc.description.abstract
Many methods are available for multivariate outlier detection but until now only a hand full are developed for spatial data where there might be observations differing from their neighbors, so-called local outliers. There are methods based on a pairwise Mahalanobis distance approach, however the type of the covariance matrices used is not yet agreed upon and covers only a global covariance (Filzmoser et al. (2013)) and a very local covariance structure (Ernst and Haesbroeck (2016)), more precisely one covariance estimation per observation.
To bridge the gap between the global and local approach by providing a refined covariance structure we develop spatially smoothed robust and regular covariance matrices based on the MRCD estimator (Boudt et al. (2020)) for pre-defined neighborhoods. As well known from the MCD literature, a subset of observations, the so-called H-set, is obtained by optimizing an objective function. In our case we obtain a set of optimal H-sets from minimizing an objective function which is based on a linear spatial smoothing design of local covariance matrices.
A heuristic algorithm based on the notion of a C-step is developed to find the optimal set of H-sets which also shows stable convergence properties in general. We demonstrate the applicability of the new covariance estimators and the importance of a compromise between locality and globality for local outlier detection with simulated and real world data including measurements of Austrian weather stations and further compare the performance with other state-of-the-art methods from statistics and machine learning.
en
dc.description.sponsorship
European Commission
-
dc.language.iso
en
-
dc.subject
Local outlier detection
en
dc.subject
Multivariate data
en
dc.subject
Spatial data
en
dc.subject
MRCD estimation
en
dc.title
Detecting Local Outliers Using the Spatially Smoothed MRCD Estimator
en
dc.type
Presentation
en
dc.type
Vortrag
de
dc.relation.grantno
SEMACRET - 101057741 - GAP-101057741
-
dc.type.category
Conference Presentation
-
tuw.project.title
Sustainable exploration for orthomagmatic (critical) raw materials in the EU: Charting the road to the green energy transition.
