Community mobility in the European regions during COVID-19 pandemic: A partitioning around medoids with noise cluster based on space-time autoregressive models

Abstract

In this paper we propose a robust fuzzy clustering model, the STAR-based Fuzzy C-Medoids Clustering model with Noise Cluster, to define territorial partitions of the European regions (NUTS2) according to the workplaces mobility trends for places of work provided by Google with reference to the whole COVID-19 pandemic period. The clustering model takes into account both temporal and spatial information by means of the autoregressive temporal and spatial coefficients of the STAR model. The proposed clustering model through the noise cluster is capable of neutralizing the negative effects of noisy data. The main empirical results regard the expected direct relationship between the Community mobility trend and the lockdown periods, and a clear spatial interaction effect among neighboring regions.

Keywords: COVID-19 outbreak; Fuzzy C-medoids clustering; Google COVID-19 community mobility report; NUTS 2; Robust clustering; STAR model.

Fig. 1

Spatial distribution by decile range for the mean percentage variations (change from baseline) of workplace mobility in March 2020.

Fig. 2

FS values on varying $C$, for each time window.

Fig. 3

Ternary plots of membership degrees for clustering results referred to the first, second and third time window.

Fig. 4

Ternary plots of membership degrees for clustering results referred to the fourth time window and to the whole one.

Fig. 5

Muldidimensional scaling projection on two dimensions (on the left) and tridimensional representation (on the right) of the model coefficients by groups — First time window.

Fig. 6

Multidimensional scaling projection on two dimensions (on the left) and tridimensional representation (on the right) of the model coefficients by groups — Second time window.

Fig. 7

Multidimensional scaling projection on two dimensions (on the left) and tridimensional representation (on the right) of the model coefficients by groups — Third time window.

Fig. 8

Multidimensional scaling projection on two dimensions (on the left) and tridimensional representation (on the right) of the model coefficients by groups — Fourth time window.

Fig. 9

Multidimensional scaling projection on two dimensions (on the left) and tridimensional representation (on the right) of the model coefficients by groups — Whole time window.

Fig. 10

Violin plots for Clusters 1 e 2 — First time window.

Fig. 11

Violin plots for Clusters 1 e 2 — Second time window.

Fig. 12

Violin plots for Clusters 1 e 2 — Third time window.

Fig. 13

Violin plots for Clusters 1 e 2 — Fourth time window.

Fig. 14

Violin plots for Clusters 1 e 2 — Whole time window.

Fig. 15

Map of clustering results — Whole time window.

Fig. 16

Map of clustering results — First time window.

Fig. 17

Map of clustering results — Second time window.

Fig. 18

Map of clustering results — Third time window.

Fig. 19

Map of clustering results — Fourth time window.