Spatial PCA-based fuzzy clustering (MULTISPATI-PCA)

Performs clustering of spatial data using a combination of spatial Principal Component Analysis (PCA), and fuzzy k-means clustering.

The workflow consists of:

Dimensionality reduction using spatial PCA
Selection of components based on explained spatial variance
Fuzzy clustering over selected components

Usage

kmspc(
  data,
  variables,
  number_cluster = 3:5,
  explainedVariance = 70,
  ldist = 0,
  udist = 40,
  center = TRUE,
  fuzzyness = 1.2,
  distance = "euclidean",
  zero.policy = FALSE,
  only_spca_results = TRUE,
  all_results = FALSE
)

Arguments

data

an sf object with point geometries

variables

character vector with variable names used for clustering. If missing, all numeric variables in data are used.

number_cluster

numeric vector indicating the number of clusters to evaluate (e.g., 3:5)

explainedVariance

numeric. Percentage (0–100) of cumulative explained spatial variance used to select spatial principal components. Values between 0 and 1 are interpreted as proportions.

ldist, udist

numeric. Lower and upper distance thresholds used to define spatial neighbors.

center

centering option passed to PCA:

TRUE: center variables by their mean
FALSE: no centering
numeric: custom centering vector

fuzzyness

numeric value greater than 1 controlling the degree of fuzziness in clustering (see e1071::cmeans)

distance

character distance metric for clustering. One of "euclidean" or "manhattan" (abbreviations allowed)

zero.policy

Logical. If TRUE, allows empty neighbor sets; if FALSE, stops with an error.

only_spca_results

logical. If TRUE, only spatial PCA results are returned. If FALSE, both PCA and spatial PCA summaries are included.

all_results

logical. If TRUE, full PCA and spatial PCA objects are returned (can increase computation time and memory use).

Value

A list with the following elements:

cluster: data.frame with cluster assignments for each evaluated number of clusters
indices: data.frame with clustering validity indices
summaryResults: data.frame with clustering metrics (iterations, SSDW)
pca_results: (optional) PCA and/or spatial PCA summaries depending on arguments

Details

Spatial relationships are defined using distance-based neighbors (spdep::dnearneigh). These relationships are incorporated into the spatial PCA analysis to extract spatially structured components.

Clustering is performed using fuzzy c-means over selected spatial components. Several indices are computed to help determine the optimal number of clusters:

Xie-Beni index
Partition coefficient
Partition entropy
Summary index (normalized combination)

Examples

library(sf)
data(wheat, package = 'paar')

# Transform the data.frame into a sf object
wheat_sf <- st_as_sf(wheat, coords = c('x', 'y'), crs = 32720)

# Run the kmspc function
kmspc_results <- kmspc(wheat_sf, number_cluster = 2:4)
#> Warning: All numeric Variables will be used to make clusters

# Print the summaryResults
kmspc_results$summaryResults
#>   Clusters Iterations      SSDW
#> 1        2         18 1.8713082
#> 2        3         56 1.3057409
#> 3        4         23 0.9948927

# Print the indices
kmspc_results$indices
#>   Num. Cluster     Xie Beni Partition Coefficient Entropy of Partition
#> 1            2 3.520996e-05             0.9611975           0.06490128
#> 2            3 5.479347e-05             0.9391130           0.10430426
#> 3            4 5.827060e-05             0.9293032           0.12351250
#>   Summary Index
#> 1      1.281105
#> 2      1.597481
#> 3      1.713107

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

# Combine the results in a single object
wheat_clustered <- cbind(wheat_sf, kmspc_results$cluster)

# Plot the results
plot(wheat_clustered[, "Cluster_2"])