Zone delineation

library(paar)
library(sf)
require(ggplot2)

Multivariate zone delineation can be done using kmspc function, whereas univariate zone delineation can be done with fyzzy_k_means function.

Multivariate function implements the protocol proposed by Córdoba et al. (2016), which performs a clustering with the kmeans function using as an input the spatial principal components (sPC) of the data. The function requires an sf object with the data to be clustered, and more than one numeric variable. The function by default returns a list with the following components: - summaryResults: a data.frame with - indices: a data.frame with indices to help to chose the optimal number of clusters. - cluster: the cluster number assigned to each observation.

For this example we will use the wheat dataset that comes with the paar package. The data.frame has apparent electrical conductivity (ECa) measured at two depths, elevation data, soil depth, and wheat gran yield. All variables have been interpolated to an unique grid and then merged in a single data.frame.

data(wheat, package = 'paar')

wheat_sf <- st_as_sf(wheat,
                     coords = c('x', 'y'),
                     crs = 32720)

plot(wheat_sf)

The function kmspc requires the sf object with the data to be clustered, and the number of clusters (zones) to be delineated. For the sPC process, is necessary to specify the distance in which observations will be considered neighbors. The ldist and udist arguments specify the lower and upper distance thresholds, respectively. The explainedVariance argument specifies the minimum value of explained variance that the Principal Component to be used for the cluster process should explain. The center argument specifies if the data should be centered before the sPC process (default TRUE).

# Run the kmspc function
kmspc_results <- 
  kmspc(wheat_sf,
        number_cluster = 2:4,
        explainedVariance = 70,
        ldist = 0,
        udist = 40,
        center = TRUE)
#> Warning: All numeric Variables will be used to make clusters

To help the user to chose the optimal number of clusters, the function returns a data.frame with indices (Xie Beni, Partition Coefficient, Entropy of Partition, and Summary Index). The Summary Index is a combination of the indices to obtain a measure of the information reported by each index. In this example, the optimum number of cluster is 2. For each index, lower the value better the clustering. More information can be found in Paccioretti, Córdoba, and Balzarini (2020).

kmspc_results$indices
#>   Num. Cluster     Xie Beni Partition Coefficient Entropy of Partition
#> 1            2 3.521021e-05             0.9611971           0.06490188
#> 2            3 5.475563e-05             0.9391553           0.10423779
#> 3            4 5.826202e-05             0.9293062           0.12350679
#>   Summary Index
#> 1      1.281160
#> 2      1.596943
#> 3      1.713109

The cluster for each observation can be found in the cluster component of the kmspc object. The cluster component is a data.frame with the cluster number assigned to each observation.

head(kmspc_results$cluster)
#>      Cluster_2 Cluster_3 Cluster_4
#> [1,] "2"       "3"       "1"      
#> [2,] "2"       "3"       "1"      
#> [3,] "2"       "3"       "1"      
#> [4,] "2"       "1"       "1"      
#> [5,] "2"       "1"       "1"      
#> [6,] "2"       "1"       "1"

The clusters can be combined to the original data using the cbind function.

wheat_clustered <- cbind(wheat_sf, kmspc_results$cluster)

This cluster can be plotted with the plot function.

plot(wheat_clustered[, "Cluster_2"])

Also, ggplot can be used to plot the clusters.

ggplot(wheat_clustered) +
  geom_sf(aes(color = Cluster_2)) +
  theme_minimal()