A simulated annealing algorithm to solve the AZP problem

Source: R/clustering.R

The automatic zoning procedure (AZP) was initially outlined in Openshaw (1977) as a way to address some of the consequences of the modifiable areal unit problem (MAUP). In essence, it consists of a heuristic to find the best set of combinations of contiguous spatial units into p regions, minimizing the within sum of squares as a criterion of homogeneity. The number of regions needs to be specified beforehand.

azp_sa(
  p,
  w,
  df,
  cooling_rate,
  sa_maxit = 1,
  bound_variable = data.frame(),
  min_bound = 0,
  inits = 0,
  initial_regions = vector("numeric"),
  scale_method = "standardize",
  distance_method = "euclidean",
  random_seed = 123456789,
  rdist = numeric()
)

Arguments

p

The number of spatially constrained clusters

w

An instance of Weight class

df

A data frame with selected variables only. E.g. guerry[c("Crm_prs", "Crm_prp", "Litercy")]

cooling_rate

The cooling rate of a simulated annealing algorithm. Defaults to 0.85

sa_maxit

(optional): The number of iterations of simulated annealing. Defaults to 1

bound_variable

(optional) A data frame with selected bound variabl

min_bound

(optional) A minimum bound value that applies to all clusters

inits

(optional) The number of construction re-runs, which is for ARiSeL "automatic regionalization with initial seed location"

initial_regions

(optional) The initial regions that the local search starts with. Default is empty. means the local search starts with a random process to "grow" clusters

scale_method

(optional) One of the scaling methods ('raw', 'standardize', 'demean', 'mad', 'range_standardize', 'range_adjust') to apply on input data. Default is 'standardize' (Z-score normalization).

distance_method

(optional) The distance method used to compute the distance betwen observation i and j. Defaults to "euclidean". Options are "euclidean" and "manhattan"

random_seed

(optional) The seed for random number generator. Defaults to 123456789.

rdist

(optional) The distance matrix (lower triangular matrix, column wise storage)

Value

A names list with names "Clusters", "Total sum of squares", "Within-cluster sum of squares", "Total within-cluster sum of squares", and "The ratio of between to total sum of squares".

Examples

if (FALSE) { # \dontrun{
library(sf)
guerry_path <- system.file("extdata", "Guerry.shp", package = "rgeoda")
guerry <- st_read(guerry_path)
queen_w <- queen_weights(guerry)
data <- guerry[c('Crm_prs','Crm_prp','Litercy','Donatns','Infants','Suicids')]
azp_clusters <- azp_sa(5, queen_w, data, cooling_rate = 0.85)
azp_clusters
} # }