__author__ = "Xun Li <lixun910@gmail.com>"
from ..libgeoda import VecVecDouble, VecPair, VecDouble, VecInt, Pair
from ..libgeoda import gda_azp_greedy, gda_azp_sa, gda_azp_tabu
from ..libgeoda import gda_betweensumofsquare, gda_totalsumofsquare, gda_withinsumofsquare, flat_2dclusters
'''
Changes:
1/20/2021 Add azp_greedy, _sa, azp_tabu
'''
[docs]def azp_greedy(p, w, data, **kwargs):
''' A greedy algorithm to solve the AZP problem
Note:
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.
Arguments:
p (int): The number of spatially constrained clusters
w (Weight): an instance of Weight class
data (tuple): A list of numeric vectors of selected variable
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
Returns:
list: A list of numeric vectors represents a group of clusters
'''
min_bound = 0 if 'min_bound' not in kwargs else kwargs['min_bound']
bound_variable = [] if 'bound_variable' not in kwargs else kwargs['bound_variable']
inits = 0 if 'inits' not in kwargs else kwargs['inits']
init_regions = [] if 'init_regions' not in kwargs else kwargs['init_regions']
scale_method = "standardize" if "scale_method" not in kwargs else kwargs['scale_method']
distance_method = 'euclidean' if 'distance_method' not in kwargs else kwargs['distance_method']
random_seed = 123456789 if 'random_seed' not in kwargs else kwargs['random_seed']
if w.num_obs < 1:
raise ValueError("The weights is not valid.")
if p < 1 or p > w.num_obs:
raise ValueError("The number of clusters should be a positive integer.")
if len(data) < 1:
raise ValueError("The data from selected variable is empty.")
in_data = VecVecDouble()
if type(data).__name__ == "DataFrame":
data = data.values.transpose().tolist()
for d in data:
in_data.push_back(d)
min_bounds = VecPair()
max_bounds = VecPair()
if min_bound > 0 and len(bound_variable) == w.num_obs:
min_bounds.push_back((min_bound, list(bound_variable)))
in_init_regions = VecInt(list(init_regions))
cluster_ids = gda_azp_greedy(p, w.gda_w, in_data, scale_method, inits, min_bounds, max_bounds, in_init_regions, distance_method, random_seed)
between_ss = gda_betweensumofsquare(cluster_ids, in_data)
total_ss = gda_totalsumofsquare(in_data)
ratio = between_ss / total_ss
within_ss = gda_withinsumofsquare(cluster_ids, in_data)
return {
"Total sum of squares" : total_ss,
"Within-cluster sum of squares" : within_ss,
"Total within-cluster sum of squares" : between_ss,
"The ratio of between to total sum of squares" : ratio,
"Clusters" : flat_2dclusters(w.num_obs, cluster_ids),
}
[docs]def azp_sa(p, w, data, cooling_rate=0.85, **kwargs):
''' A simulated annealing algorithm to solve the AZP problem
Note:
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.
Arguments:
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
Returns:
list: A list of numeric vectors represents a group of clusters
'''
sa_maxit = 1 if 'sa_maxit' not in kwargs else kwargs['sa_maxit']
min_bound = 0 if 'min_bound' not in kwargs else kwargs['min_bound']
bound_variable = [] if 'bound_variable' not in kwargs else kwargs['bound_variable']
inits = 0 if 'inits' not in kwargs else kwargs['inits']
init_regions = [] if 'init_regions' not in kwargs else kwargs['init_regions']
scale_method = "standardize" if "scale_method" not in kwargs else kwargs['scale_method']
distance_method = 'euclidean' if 'distance_method' not in kwargs else kwargs['distance_method']
random_seed = 123456789 if 'random_seed' not in kwargs else kwargs['random_seed']
if cooling_rate <=0 or cooling_rate >=1:
raise ValueError("Cooling rate should be in range (0,1).")
if w.num_obs < 1:
raise ValueError("The weights is not valid.")
if p < 1 or p > w.num_obs:
raise ValueError("The number of clusters should be a positive integer.")
if len(data) < 1:
raise ValueError("The data from selected variable is empty.")
in_data = VecVecDouble()
if type(data).__name__ == "DataFrame":
data = data.values.transpose().tolist()
for d in data:
in_data.push_back(d)
min_bounds = VecPair()
max_bounds = VecPair()
if min_bound > 0 and len(bound_variable) == w.num_obs:
min_bounds.push_back((min_bound, list(bound_variable)))
in_init_regions = VecInt(list(init_regions))
cluster_ids = gda_azp_sa(p, w.gda_w, in_data, scale_method, inits, cooling_rate, sa_maxit, min_bounds, max_bounds, in_init_regions, distance_method, random_seed)
between_ss = gda_betweensumofsquare(cluster_ids, in_data)
total_ss = gda_totalsumofsquare(in_data)
ratio = between_ss / total_ss
within_ss = gda_withinsumofsquare(cluster_ids, in_data)
return {
"Total sum of squares" : total_ss,
"Within-cluster sum of squares" : within_ss,
"Total within-cluster sum of squares" : between_ss,
"The ratio of between to total sum of squares" : ratio,
"Clusters" : flat_2dclusters(w.num_obs, cluster_ids),
}
[docs]def azp_tabu(p, w, data, tabu_length, **kwargs):
''' A tabu-search algorithm to solve the AZP problem
Note:
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.
Arguments:
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']]
tabu_length (int): The length of a tabu search heuristic of tabu algorithm. Defaults to 10.
conv_tabu (int, optional): The number of non-improving moves. Defaults to 10.
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
Returns:
list: A list of numeric vectors represents a group of clusters
'''
conv_tabu = 10 if 'conv_tabu' not in kwargs else kwargs['conv_tabu']
min_bound = 0 if 'min_bound' not in kwargs else kwargs['min_bound']
bound_variable = [] if 'bound_variable' not in kwargs else kwargs['bound_variable']
inits = 0 if 'inits' not in kwargs else kwargs['inits']
init_regions = [] if 'init_regions' not in kwargs else kwargs['init_regions']
scale_method = "standardize" if "scale_method" not in kwargs else kwargs['scale_method']
distance_method = 'euclidean' if 'distance_method' not in kwargs else kwargs['distance_method']
random_seed = 123456789 if 'random_seed' not in kwargs else kwargs['random_seed']
if w.num_obs < 1:
raise ValueError("The weights is not valid.")
if p < 1 or p > w.num_obs:
raise ValueError("The number of clusters should be a positive integer.")
if len(data) < 1:
raise ValueError("The data from selected variable is empty.")
in_data = VecVecDouble()
if type(data).__name__ == "DataFrame":
data = data.values.transpose().tolist()
for d in data:
in_data.push_back(d)
min_bounds = VecPair()
max_bounds = VecPair()
if min_bound > 0 and len(bound_variable) == w.num_obs:
min_bounds.push_back((min_bound, list(bound_variable)))
in_init_regions = VecInt(list(init_regions))
cluster_ids = gda_azp_tabu(p, w.gda_w, in_data, scale_method, inits, tabu_length, conv_tabu, min_bounds, max_bounds, in_init_regions, distance_method, random_seed)
between_ss = gda_betweensumofsquare(cluster_ids, in_data)
total_ss = gda_totalsumofsquare(in_data)
ratio = between_ss / total_ss
within_ss = gda_withinsumofsquare(cluster_ids, in_data)
return {
"Total sum of squares" : total_ss,
"Within-cluster sum of squares" : within_ss,
"Total within-cluster sum of squares" : between_ss,
"The ratio of between to total sum of squares" : ratio,
"Clusters" : flat_2dclusters(w.num_obs, cluster_ids),
}