def assert_feasible(solution, adj, n_regions=None):
"""
Parameters
----------
solution : :class:`numpy.ndarray`
Array of region labels.
adj : :class:`scipy.sparse.csr_matrix`
Adjacency matrix representing the contiguity relation.
n_regions : `int` or `None`
An `int` represents the desired number of regions.
If `None`, then the number of regions is not checked.
Raises
------
exc : `ValueError`
A `ValueError` is raised if clustering is not spatially contiguous.
Given the `n_regions` argument is not `None`, a `ValueError` is raised
also if the number of regions is not equal to the `n_regions` argument.
"""
if n_regions is not None:
if len(set(solution)) != n_regions:
raise ValueError(
"The number of regions is {} but "
"should be {}".format(len(solution), n_regions)
)
for region_label in set(solution):
aux = sub_adj_matrix(adj, np.where(solution == region_label)[0])
# check right contiguity
if not is_connected(aux):
raise ValueError(
"Region {} is not spatially " "contiguous.".format(region_label)
)
def fit_from_scipy_sparse_matrix(
self,
adj,
attr,
n_regions,
initial_labels=None,
objective_func=ObjectiveFunctionPairwise()):
"""
Perform the AZP algorithm as described in [OR1995]_.
The resulting region labels are assigned to the instance's
:attr:`labels_` attribute.
Parameters
----------
adj : :class:`scipy.sparse.csr_matrix`
Adjacency matrix representing the contiguity relation.
attr : :class:`numpy.ndarray`
Array (number of areas x number of attributes) of areas' attributes
relevant to clustering.
n_regions : `int`
Number of desired regions.
initial_labels : :class:`numpy.ndarray` or None, default: None
One-dimensional array of labels at the beginning of the algorithm.
If None, then a random initial clustering will be generated.
objective_func : :class:`region.objective_function.ObjectiveFunction`, default: ObjectiveFunctionPairwise()
The objective function to use.
"""
if attr.ndim == 1:
attr = attr.reshape(adj.shape[0], -1)
self.allow_move_strategy.attr_all = attr
self.objective_func = objective_func
# step 1
if initial_labels is not None:
assert_feasible(initial_labels, adj, n_regions)
initial_labels_gen = separate_components(adj, initial_labels)
else:
initial_labels_gen = generate_initial_sol(adj, n_regions)
labels = -np.ones(adj.shape[0])
for labels_comp in initial_labels_gen:
comp_idx = np.where(labels_comp != -1)[0]
adj_comp = sub_adj_matrix(adj, comp_idx)
labels_comp = labels_comp[comp_idx]
attr_comp = attr[comp_idx]
self.allow_move_strategy.start_new_component(
labels_comp, attr_comp, self.objective_func, comp_idx)
labels_comp = self._azp_connected_component(
adj_comp, labels_comp, attr_comp)
labels[comp_idx] = labels_comp
self.n_regions = n_regions
self.labels_ = labels
def boolean_assert_feasible(solution, adj, n_regions=None):
"""
Return boolean version of assert_feasible
"""
resp = []
if n_regions is not None:
if len(set(solution)) != n_regions:
raise ValueError(
"The number of regions is {} but "
"should be {}".format(len(solution), n_regions)
)
for region_label in set(solution):
aux = sub_adj_matrix(adj, np.where(solution == region_label)[0])
resp.append(is_connected(aux))
final_resp = all(resp)
return final_resp
def _azp_connected_component(self, adj, initial_labels, attr):
"""
Implementation of the reactive tabu version of the AZP algorithm (refer
to [OR1995]_) for a spatially connected set of areas (i.e. for every
area there is a path to every other area).
Parameters
----------
adj : :class:`scipy.sparse.csr_matrix`
Refer to the corresponding argument in
:meth:`AZP._azp_connected_component`.
initial_labels : :class:`numpy.ndarray`
Refer to the corresponding argument in
:meth:`AZP._azp_connected_component`.
attr : :class:`numpy.ndarray`
Refer to the corresponding argument in
:meth:`AZP._azp_connected_component`.
Returns
-------
labels : :class:`numpy.ndarray`
Refer to the return value in :meth:`AZP._azp_connected_component`.
"""
self.reset_tabu(1)
# if there is only one region in the initial solution, just return it.
distinct_regions = list(np.unique(initial_labels))
if len(distinct_regions) == 1:
return initial_labels
# step 2: make a list of the M regions
labels = initial_labels
it_since_tabu_len_changed = 0
obj_val_start = float("inf")
# step 12: Repeat steps 3-11 until either no further improvements are
# made or a maximum number of iterations are exceeded.
for it in range(self.maxit):
obj_val_end = self.objective_func(labels, attr)
if not obj_val_end < obj_val_start:
break # step 12
obj_val_start = obj_val_end
it_since_tabu_len_changed += 1
# step 3: Define the list of all possible moves that are not tabu
# and retain regional connectivity.
possible_moves = []
for area in range(labels.shape[0]):
old_region = labels[area]
sub_adj = sub_adj_matrix(
adj, np.where(labels == old_region)[0], wo_nodes=area)
# moving the area must not destroy spatial contiguity in donor
# region and if area is alone in its region, it must stay:
if is_connected(sub_adj) and count(labels, old_region) > 1:
for neigh in neighbors(adj, area):
new_region = labels[neigh]
if new_region != old_region:
possible_move = Move(area, old_region, new_region)
if possible_move not in self.tabu:
possible_moves.append(possible_move)
# step 4: Find the best nontabu move.
best_move = None
best_move_index = None
best_objval_diff = float("inf")
for i, move in enumerate(possible_moves):
obj_val_diff = self.objective_func.update(
move.area, move.new_region, labels, attr)
if obj_val_diff < best_objval_diff:
best_move_index, best_move = i, move
best_objval_diff = obj_val_diff
# step 5: Make the move. Update the tabu status.
self._make_move(best_move.area, best_move.new_region, labels)
# step 6: Look up the current zoning system in a list of all zoning
# systems visited so far during the search. If not found then go
# to step 10.
# Sets can't be permuted so we convert our list to a set:
label_tup = tuple(labels)
if label_tup in self.visited:
# step 7: If it is found and it has been visited more than K1
# times already and this cyclical behavior has been found on
# at least K2 other occasions (involving other zones) then go
# to step 11.
times_visited = self.visited.count(label_tup)
cycle = list(reversed(self.visited))
cycle = cycle[:cycle.index(label_tup) + 1]
cycle = list(reversed(cycle))
it_until_repetition = len(cycle)
if times_visited > self.k1:
times_cycle_found = 0
if self.k2 > 0:
for i in range(len(self.visited) - len(cycle)):
if self.visited[i:i + len(cycle)] == cycle:
times_cycle_found += 1
if times_cycle_found >= self.k2:
break
if times_cycle_found >= self.k2:
# step 11: Delete all stored zoning systems and make P
# random moves, P = 1 + self.avg_it_until_rep/2, and
# update tabu to preclude a return to the previous
# state.
# we save the labels such that we can access it if
# this step yields a poor solution.
last_step = (11, tuple(labels))
self.visited = []
p = math.floor(1 + self.avg_it_until_rep / 2)
possible_moves.pop(best_move_index)
for _ in range(p):
move = possible_moves.pop(
random.randrange(len(possible_moves)))
self._make_move(move.area, move.new_region, labels)
continue
# step 8: Update a moving average of the repetition
# interval self.avg_it_until_rep, and increase the
# prohibition period R to 1.1*R.
self.rep_counter += 1
avg_it = self.avg_it_until_rep
self.avg_it_until_rep = 1 / self.rep_counter * \
((self.rep_counter-1)*avg_it + it_until_repetition)
self.tabu = deque(self.tabu, 1.1 * self.tabu.maxlen)
# step 9: If the number of iterations since R was last
# changed exceeds self.avg_it_until_rep, then decrease R to
# max(0.9*R, 1).
if it_since_tabu_len_changed > self.avg_it_until_rep:
new_tabu_len = max([0.9 * self.tabu.maxlen, 1])
new_tabu_len = math.floor(new_tabu_len)
self.tabu = deque(self.tabu, new_tabu_len)
it_since_tabu_len_changed = 0 # step 8
# step 10: Save the zoning system and go to step 12.
self.visited.append(tuple(labels))
last_step = 10
if last_step == 10:
try:
return np.array(self.visited[-2])
except IndexError:
return np.array(self.visited[-1])
# if step 11 was the last one, the result is in last_step[1]
return np.array(last_step[1])
def _azp_connected_component(self, adj, initial_clustering, attr):
"""
Implementation of the basic tabu version of the AZP algorithm (refer
to [OR1995]_) for a spatially connected set of areas (i.e. for every
area there is a path to every other area).
Parameters
----------
adj : :class:`scipy.sparse.csr_matrix`
Refer to the corresponding argument in
:meth:`AZP._azp_connected_component`.
initial_clustering : :class:`numpy.ndarray`
Refer to the corresponding argument in
:meth:`AZP._azp_connected_component`.
attr : :class:`numpy.ndarray`
Refer to the corresponding argument in
:meth:`AZP._azp_connected_component`.
Returns
-------
labels : :class:`numpy.ndarray`
Refer to the return value in :meth:`AZP._azp_connected_component`.
"""
self.reset_tabu()
# if there is only one region in the initial solution, just return it.
distinct_regions = list(np.unique(initial_clustering))
if len(distinct_regions) == 1:
return initial_clustering
# step 2: make a list of the M regions
labels = initial_clustering
visited = []
stop = False
while True:
# added termination condition (not in Openshaw & Rao (1995))
label_tup = tuple(labels)
if visited.count(label_tup) >= self.reps_before_termination:
stop = True
visited.append(label_tup)
# step 1 Find the global best move that is not prohibited or tabu.
# find possible moves (globally)
best_move = None
best_objval_diff = float("inf")
for area in range(labels.shape[0]):
old_region = labels[area]
sub_adj = sub_adj_matrix(
adj, np.where(labels == old_region)[0], wo_nodes=area)
# moving the area must not destroy spatial contiguity in donor
# region and if area is alone in its region, it must stay:
if is_connected(sub_adj) and count(labels, old_region) > 1:
for neigh in neighbors(adj, area):
new_region = labels[neigh]
if new_region != old_region:
possible_move = Move(area, old_region, new_region)
if possible_move not in self.tabu:
objval_diff = self.objective_func.update(
possible_move.area,
possible_move.new_region, labels, attr)
if objval_diff < best_objval_diff:
best_move = possible_move
best_objval_diff = objval_diff
# step 2: Make this move if it is an improvement or equivalet in
# value.
if best_move is not None and best_objval_diff <= 0:
self._make_move(best_move.area, best_move.new_region, labels)
else:
# step 3: if no improving move can be made, then see if a tabu
# move can be made which improves on the current local best
# (termed an aspiration move)
improving_tabus = [
move for move in self.tabu
if labels[move.area] == move.old_region
and self.objective_func.update(move.area, move.new_region,
labels, attr) < 0
]
if improving_tabus:
aspiration_move = random_element_from(improving_tabus)
self._make_move(aspiration_move.area,
aspiration_move.new_region, labels)
else:
# step 4: If there is no improving move and no aspirational
# move, then make the best move even if it is nonimproving
# (that is, results in a worse value of the objective
# function).
if stop:
break
if best_move is not None:
self._make_move(best_move.area, best_move.new_region,
labels)
return labels
def _azp_connected_component(self, adj, initial_clustering, attr):
"""
Implementation of the AZP algorithm for a spatially connected set of
areas (i.e. for every area there is a path to every other area).
Parameters
----------
adj : :class:`scipy.sparse.csr_matrix`
Adjacency matrix representing the contiguity relation. The matrix'
shape is (N, N) where N denotes the number of areas in the
currently considered connected component.
initial_clustering : :class:`numpy.ndarray`
Array of labels. Shape: (N,) where N denotes the number of areas in
the currently considered connected component.
attr : :class:`numpy.ndarray`
Array of labels. Shape: (N, M) where N denotes the number of areas
in the currently considered connected component and M denotes the
number of attributes per area.
Returns
-------
labels : :class:`numpy.ndarray`
One-dimensional array of region labels after the AZP algorithm has
been performed. Only region labels of the currently considered
connected component are returned.
"""
# if there is only one region in the initial solution, just return it.
distinct_regions = list(np.unique(initial_clustering))
if len(distinct_regions) == 1:
return initial_clustering
distinct_regions_copy = distinct_regions.copy()
# step 2: make a list of the M regions
labels = initial_clustering
obj_val_start = float("inf")
obj_val_end = self.allow_move_strategy.objective_val
region_neighbors = {}
for region in distinct_regions:
region_areas = set(np.where(labels == region)[0])
neighs = set()
for area in region_areas:
neighs.update(neighbors(adj, area))
region_neighbors[region] = neighs.difference(region_areas)
del neighs
# step 7: Repeat until no further improving moves are made
while obj_val_end < obj_val_start: # improvement
obj_val_start = float(obj_val_end)
distinct_regions = distinct_regions_copy.copy()
# step 6: when the list for region K is exhausted return to step 3
# and select another region and repeat steps 4-6
while distinct_regions:
# step 3: select & remove any region K at random from this list
recipient = pop_randomly_from(distinct_regions)
while True:
# step 4: identify a set of zones bordering on members of
# region K that could be moved into region K without
# destroying the internal contiguity of the donor region(s)
candidates = []
for neigh in region_neighbors[recipient]:
neigh_region = labels[neigh]
sub_adj = sub_adj_matrix(
adj,
np.where(labels == neigh_region)[0],
wo_nodes=neigh)
if is_connected(sub_adj):
# if area is alone in its region, it must stay
if count(labels, neigh_region) > 1:
candidates.append(neigh)
# step 5: randomly select zones from this list until either
# there is a local improvement in the current value of the
# objective function or a move that is equivalently as good
# as the current best. Then make the move, update the list
# of candidate zones, and return to step 4 or else repeat
# step 5 until the list is exhausted.
while candidates:
cand = pop_randomly_from(candidates)
if self.allow_move_strategy(cand, recipient, labels):
donor = labels[cand]
make_move(cand, recipient, labels)
region_neighbors[donor].add(cand)
region_neighbors[recipient].discard(cand)
neighs_of_cand = neighbors(adj, cand)
recipient_region_areas = set(
np.where(labels == recipient)[0])
region_neighbors[recipient].update(neighs_of_cand)
region_neighbors[recipient].difference_update(
recipient_region_areas)
donor_region_areas = set(
np.where(labels == donor)[0])
not_donor_neighs_anymore = set(
area for area in neighs_of_cand if not any(
a in donor_region_areas
for a in neighbors(adj, area)))
region_neighbors[donor].difference_update(
not_donor_neighs_anymore)
break
else:
break
obj_val_end = float(self.allow_move_strategy.objective_val)
return labels