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weighted_kmeans.py
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weighted_kmeans.py
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''' Defines the Weighted K-Means class that can be called in a similar fashion as scikit-learn kmeans,
and the evaluation function eval_error for observing the performance of a certain redistricting
Dependencies: numpy, copy and geopy.distance
'''
import numpy as np
import copy
from geopy.distance import great_circle
class Weighted_K_Means:
def __init__(self, k=13, tolerance=0.0001, max_iterations=50,
weight_by_pop=False, weight_by_race=False, weight_by_dem=False):
self.k = k
self.tolerance = tolerance
self.max_iterations = max_iterations
self.weight_by_pop = weight_by_pop
self.weight_by_race = weight_by_race
self.weight_by_dem = weight_by_dem
def distance(self, point_1, point_2):
return great_circle(point_1, point_2).km
def fit(self, VTD_centers, population, black_population, dem_votes, total_votes,
beta=0.5, alpha_pop=0.0, alpha_race=0.0, alpha_dem=0.0):
self.VTD_centers = VTD_centers
self.population = population
self.black_population = black_population
self.dem_votes = dem_votes
self.total_votes = total_votes
# 1. initialize centoroids at k random VTDs
self.centroid_idx = np.random.choice(VTD_centers.id.values, size=self.k, replace=False)
self.centroids = VTD_centers.iloc[self.centroid_idx, 1:].values
# 2. initialize weights at 1/k
self.weights = [1 / self.k for i in range(self.k)]
self.total_population = sum(population)
for iteration in range(self.max_iterations):
self.clusters = {} # stores actual lat long of each VTD assigned per cluster
self.clusters_by_ids = {} # stores the id of each VTD assigned per cluster
for i in range(self.k):
self.clusters[i] = []
self.clusters_by_ids[i] = []
# 3. find the distance between the point and cluster; choose the nearest centroid
for VTD in self.VTD_centers.values:
VTD_id = int(VTD[0])
VTD_latlong = VTD[1:]
# 3.1 calculate distances and weigh them
distances = [self.distance(VTD_latlong, centroid) for centroid in self.centroids]
weighted_distances = [d * w for d, w in zip(distances, self.weights)]
# 3.2 find the closest cluster and assign the VTD to it as well as store its id
cluster = weighted_distances.index(min(weighted_distances))
self.clusters[cluster].append(VTD_latlong)
self.clusters_by_ids[cluster].append(VTD_id)
# 3.3 save old centroids to compare the improvement later
previous = self.centroids.copy()
# 4. average the cluster datapoints to re-calculate the centroids
for cluster in self.clusters:
self.centroids[cluster] = np.average(self.clusters[cluster], axis=0)
# 5. check how far the centroids have moved
isOptimal = True
for i in range(len(self.centroids)):
original_centroid = previous[i]
curr = self.centroids[i]
if np.sum(np.abs((curr - original_centroid) / original_centroid * 100.0)) > self.tolerance:
isOptimal = False
# 5.1 break out if the centroids don't change their positions much
if isOptimal:
print('optimal after ' + str(iteration) + ' iterations')
convergence = True
break
# 5.2 if the centroids still change a lot by the last iteration, we assume it converged
if iteration == self.max_iterations - 1:
convergence = True
# 6. update the weights
old_weights = copy.deepcopy(self.weights)
for i in self.clusters:
new_weight = 1
if self.weight_by_pop:
new_weight *= sum(population[self.clusters_by_ids[i]]) ** alpha_pop
if self.weight_by_race:
new_weight *= sum(black_population[self.clusters_by_ids[i]]) ** alpha_race
if self.weight_by_dem:
if len(self.clusters_by_ids[i]) > 1:
new_weight *= (sum(dem_votes[self.clusters_by_ids[i]]) / sum(
total_votes[self.clusters_by_ids[i]])) ** alpha_dem
else:
convergence = False
break
self.weights[i] = new_weight
for i in self.clusters:
self.weights[i] /= sum(self.weights)
# 6.1 gradually update the weights
self.weights[i] = beta * self.weights[i] + (1 - beta) * old_weights[i]
return self.clusters, self.clusters_by_ids, convergence
def eval_error(clusters_by_ids, population, black_population, dem_votes, total_votes,
k=13, weight_pop=1., weight_race=1., weight_dem=1.):
fair_population = sum(population) / k
fair_share_black = sum(black_population) / sum(population)
fair_share_dem = sum(dem_votes) / sum(total_votes)
total_error = 0
for cluster in clusters_by_ids:
pop_error = abs(sum(population[clusters_by_ids[cluster]]) - fair_population) / fair_population
race_error = abs(sum(black_population[clusters_by_ids[cluster]]) / sum(
population[clusters_by_ids[cluster]]) - fair_share_black)
dem_error = abs(
sum(dem_votes[clusters_by_ids[cluster]]) / sum(total_votes[clusters_by_ids[cluster]]) - fair_share_dem)
total_error += weight_pop * pop_error + weight_race * race_error + weight_dem * dem_error
return total_error