- Introduction (cities with coordinates)
- Calculate distance or affinity matrix
- Visualize matrix and show distance between two cities as example
- Spectral Clustering
- Find ideal number of clusters
Introduction (cities with coordinates)
#Cities_Cluster.ipynb
from geopy.geocoders import Nominatim
import time
import numpy as np
from pprint import pprint
app = Nominatim(user_agent="tutorial")
# Define 6 groups of cities, which are roughly connected
cities = ["Nairobi, Kenya", "Mombasa, Kenya", "Nakuru, Kenya", "Ruiru, Kenya", "Eldoret, Kenya", "Kisumu, Kenya",
"New York, United States", "Los Angeles, United States","Chicago, United States","Chicago, United States","Houston, United States","Phoenix, United States","San Antonio, United States",
"Kiel, Germany", "Hamburg, Germany", "Berlin, Germany", "Cologne, Germany", "Mainz, Germany", "Freiburg, Germany", "Konstanz, Germany",
"Yokohama, Japan","Kobe, Japan","Incheon, South Korea","Shanghai, China",
"Buenos Aires, Argentina","Rosario, Argentina","La Plata, Argentina","Salta, Argentina",
"Sydney, Australia","Melbourne, Australia","Brisbane, Australia","Perth, Australia","Adelaide, Australia","Hobart, Australia","Darwin, Australia"]
#for
x_ = [];
y_ = [];
citiesKM = [];
for i in range(0, len(cities)):
location = app.geocode(cities[i]).raw
#print (location['lat']);
x_.append(location['lat'])
y_.append(location['lon'])
citiesKM.append((location['lat'], location['lon']))
Calculate distance or affinity matrix
# Import the geodesic module from geopy library
from geopy.distance import geodesic as GD
# For the specified locations, load their latitude and longitude data.
#Finally, print the distance between the two sites in kilometers.
matrix = np.zeros((len(cities), len(cities)), 'float32')
for i in range(0, len(cities)):
for j in range(0, len(cities)):
if(i == j):
matrix[i,j] = 1.0;
else:
matrix[i,j] = -1.0*GD(citiesKM[i],citiesKM[j]).km
def NormalizeData(data):
return (data - np.min(data)) / (np.max(data) - np.min(data))
matrix = NormalizeData(matrix)
Visualize matrix and show distance between two cities as example
from matplotlib import pylab as plt
plt.imshow(matrix,cmap="gray")
# Import the geodesic module from geopy library
from geopy.distance import geodesic as GD
# For the specified locations, load their latitude and longitude data.
#Finally, print the distance between the two sites in kilometers.
print("The distance between Abuja and Dakar is: ", GD(citiesKM[0],citiesKM[-1]).km)
#The distance between Abuja and Dakar is: 10423.219350045409
Spectral Clustering
import scipy
from sklearn.cluster import SpectralClustering
import pandas as pd
#%%time
best_k = None
stds = {} # a map of std for each k
max_clusters = 16 # max number of clusters or target classes we are okay with
#with warnings.catch_warnings():
# warnings.simplefilter("ignore")
for clusters in range(2, max_clusters):
#print (clusters)
sc = SpectralClustering(clusters, assign_labels='cluster_qr', random_state=1, affinity='precomputed')
sc.fit_predict(matrix)
std = pd.DataFrame(sc.labels_, columns=["cluster_id"]).cluster_id.value_counts().describe().loc["std"]
stds[clusters] = std
Find ideal number of clusters
import matplotlib.pyplot as plt
import seaborn as sns
sns.set_style('darkgrid', {'axes.facecolor': '.9'})
sns.set_palette(palette='deep')
sns_c = sns.color_palette(palette='deep')
%matplotlib inline
plt.figure(figsize=(20,20))
ax = sns.barplot(x="k", y="std", data=pd.DataFrame( stds.items(), columns=["k", "std"] ))
plt.xlabel("number of clusters")
plt.ylabel("class imbalance metric (std)")
ax.grid()
