Hierarchical clustering with spatial adjacency constraints in heavy-tailed areal data

Some natural phenomena with areal/lattice data structures include extreme values or outliers. In such situations, the assumption of Gaussianity for the random field may not be reasonable, and no Gaussian transformation can be found because they exhibit heavy tails. A non-Gaussian stable random field...

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Bibliographic Details
Published in:Communications in statistics. Simulation and computation 2024-11, Vol.53 (11), p.5385-5405
Main Authors: Mousavi, Seyedeh Somayeh, Mohammadpour, Adel, Baghishani, Hossein
Format: Article
Language:English
Subjects:
Adjacency-constrained hierarchical clustering
Algorithms
Areal data
Autoregressive models
Cluster analysis
Clustering
Constraints
Criteria
Data structures
Datasets
Estuaries
Extreme values
Fields (mathematics)
Group dynamics
Multivariate analysis
Outliers (statistics)
Spatial adjacency constraints
Spatial analysis
Spatial data
Sub-Gaussian
α-Stable random field
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Summary:Some natural phenomena with areal/lattice data structures include extreme values or outliers. In such situations, the assumption of Gaussianity for the random field may not be reasonable, and no Gaussian transformation can be found because they exhibit heavy tails. A non-Gaussian stable random field, which is heavy-tailed, could be a more appropriate choice in these cases. This article introduces a sub-Gaussian α-stable (SGαS) random field for spatial analysis of multivariate areal data using a multivariate conditional autoregressive model. We, specifically, focus on the spatial clustering problem of such areal data. To address it, we develop methods that work based on adjacency constraints. To group the data, we offer an adjacency-constrained hierarchical agglomerative clustering (HAC) technique that considers both spatial and non-spatial attributes existing in the multivariate areal data. The proposed clustering algorithm is developed based on spatial adjacency constraint criteria incorporated into the HAC technique. We employed the developed algorithm to group Luxembourg communes based on simulated areal data from the SGαS distributions and French cities along the Gironde estuary based on the estuary areal dataset. We compare the results of the proposed method with the mentioned adjacency criteria, various dissimilarity, and linkages measures in clustering these two datasets.
ISSN:0361-0918
1532-4141
DOI:10.1080/03610918.2023.2184761