pygeoda.azp_sa(p, w, data, cooling_rate=0.85, **kwargs)[source]

A simulated annealing algorithm to solve the AZP problem


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.

  • p (int) – The number of spatially constrained clusters

  • w (Weight) – an instance of Weight class

  • data (list or dataframe) – A list of numeric vectors of selected variable or a data frame of selected variables e.g. guerry[[‘Crm_prs’, ‘Literacy’]]

  • cooling_rate (float) – The cooling rate of a simulated annealing algorithm. Defaults to 0.85

  • sa_maxit (int, optional) – The number of iterations of simulated annealing. Defaults to 1

  • bound_variable (tuple, optional) – A numeric vector of selected bounding variable

  • min_bound (float, optional) – A minimum value that the sum value of bounding variable int each cluster should be greater than

  • inits (int, optional) – The number of construction re-runs, which is for ARiSeL “automatic regionalization with initial seed location”

  • init_regions (tuple, 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 (str, 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 (str, optional) – The distance method used to compute the distance betwen observation i and j. Defaults to “euclidean”. Options are “euclidean” and “manhattan”

  • random_seed (int, optional) – The seed for random number generator. Defaults to 123456789. It is the same as GeoDa software

  • cpu_threads (int, optional) – The number of cpu threads used for parallel computation


A list of numeric vectors represents a group of clusters

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