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A simulated annealing algorithm to solve the AZP problem

Source: R/spatial_cluster.R
st_azp_sa.Rd

A wrapper function for rgeoda::azp_sa().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.

Usage

st_azp_sa(
  sfj,
  varcol,
  k,
  wt = NULL,
  boundvar = NULL,
  cooling_rate = 0.85,
  sa_maxit = 1,
  min_bound = 0,
  inits = 0,
  initial_regions = vector("numeric"),
  scale_method = "standardize",
  distance_method = "euclidean",
  seed = 123456789,
  rdist = numeric()
)

Arguments

sfj

An sf (simple feature) object.

varcol

The variable selected to calculate spatial lag, which is a character.

k

The number of clusters.

wt

(optional) The spatial weights object,which can use st_weights() to construct,default is constructed by st_weights(sfj,'contiguity').

boundvar

(optional) A data frame / tibble with selected bound variable.

cooling_rate

(optional) 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.

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"

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".

Author

Wenbo Lv lyu.geosocial@gmail.com

Examples

library(sf)
guerry = read_sf(system.file("extdata", "Guerry.shp", package = "rgeoda"))
guerry_clusters = st_azp_sa(guerry,c('Crm_prs','Crm_prp','Litercy','Donatns',
'Infants','Suicids'),5)
guerry_clusters
#> $Clusters
#>  [1] 5 2 3 1 1 1 2 1 2 1 1 1 2 1 4 4 3 4 2 3 3 1 2 1 2 2 3 1 1 1 1 1 3 3 3 1 2 1
#> [39] 3 3 1 3 2 1 1 1 3 3 2 2 3 2 2 3 2 3 2 2 3 2 1 1 1 1 2 2 1 2 3 3 2 2 2 2 4 2
#> [77] 1 1 1 1 4 4 4 2 2
#> 
#> $`Total sum of squares`
#> [1] 504
#> 
#> $`Within-cluster sum of squares`
#> [1] 47.86263 61.08506 29.62824 58.04068 60.31298 66.23291
#> 
#> $`Total within-cluster sum of squares`
#> [1] 180.8375
#> 
#> $`The ratio of between to total sum of squares`
#> [1] 0.3588045
#>