Can I get Cluster Centroids after Clustering the Spatial (latitude, longitude) data by DBSCAN in python

Question

DBSCAN is very different compared to k-means or k-medoids that assume clusters should have a particular shape. It assumes that clusters are group of points closely located to each other, forming a densely populated neighborhood of points in the data space.

I can calculate the mean of data points of each cluster to get the centroid of each cluster. But will it be a right process. Because concept of centroids seems feasible only for clusters with specific shape like hyperspherical.

Please answer if it is correct to calculate centroids for clusters computed by DBSCAN?

Answer 1

Try this:

# import necessary modules
import pandas as pd, numpy as np, matplotlib.pyplot as plt, time
from sklearn.cluster import DBSCAN
from sklearn import metrics
from geopy.distance import great_circle
from shapely.geometry import MultiPoint


# define the number of kilometers in one radian
kms_per_radian = 6371.0088


# load the data set
df = pd.read_csv('C:\\your_path\\summer-travel-gps-full.csv', encoding = "ISO-8859-1")
df.head()


# how many rows are in this data set?
len(df)


# scatterplot it to get a sense of what it looks like
df = df.sort_values(by=['lat', 'lon'])
ax = df.plot(kind='scatter', x='lon', y='lat', alpha=0.5, linewidth=0)

# represent points consistently as (lat, lon)
# coords = df.as_matrix(columns=['lat', 'lon'])
df_coords = df[['lat', 'lon']]
# coords = df.to_numpy(df_coords)

# define epsilon as 10 kilometers, converted to radians for use by haversine
epsilon = 10 / kms_per_radian

start_time = time.time()
db = DBSCAN(eps=epsilon, min_samples=10, algorithm='ball_tree', metric='haversine').fit(np.radians(df_coords))
cluster_labels = db.labels_
unique_labels = set(cluster_labels)

# get the number of clusters
num_clusters = len(set(cluster_labels))


# get colors and plot all the points, color-coded by cluster (or gray if not in any cluster, aka noise)
fig, ax = plt.subplots()
colors = plt.cm.rainbow(np.linspace(0, 1, len(unique_labels)))

# for each cluster label and color, plot the cluster's points
for cluster_label, color in zip(unique_labels, colors):

    size = 150
    if cluster_label == -1: #make the noise (which is labeled -1) appear as smaller gray points
        color = 'gray'
        size = 30

    # plot the points that match the current cluster label
    # X.iloc[:-1]
    # df.iloc[:, 0]
    x_coords = df_coords.iloc[:, 0]
    y_coords = df_coords.iloc[:, 1]
    ax.scatter(x=x_coords, y=y_coords, c=color, edgecolor='k', s=size, alpha=0.5)

ax.set_title('Number of clusters: {}'.format(num_clusters))
plt.show()

coefficient = metrics.silhouette_score(df_coords, cluster_labels)
print('Silhouette coefficient: {:0.03f}'.format(metrics.silhouette_score(df_coords, cluster_labels)))


# set eps low (1.5km) so clusters are only formed by very close points
epsilon = 1.5 / kms_per_radian

# set min_samples to 1 so we get no noise - every point will be in a cluster even if it's a cluster of 1
start_time = time.time()
db = DBSCAN(eps=epsilon, min_samples=1, algorithm='ball_tree', metric='haversine').fit(np.radians(df_coords))
cluster_labels = db.labels_
unique_labels = set(cluster_labels)

# get the number of clusters
num_clusters = len(set(cluster_labels))

# all done, print the outcome
message = 'Clustered {:,} points down to {:,} clusters, for {:.1f}% compression in {:,.2f} seconds'
print(message.format(len(df), num_clusters, 100*(1 - float(num_clusters) / len(df)), time.time()-start_time))



coefficient = metrics.silhouette_score(df_coords, cluster_labels)
print('Silhouette coefficient: {:0.03f}'.format(metrics.silhouette_score(df_coords, cluster_labels)))



# number of clusters, ignoring noise if present
num_clusters = len(set(cluster_labels)) #- (1 if -1 in labels else 0)
print('Number of clusters: {}'.format(num_clusters))




# create a series to contain the clusters - each element in the series is the points that compose each cluster
clusters = pd.Series([df_coords[cluster_labels == n] for n in range(num_clusters)])
clusters.tail()

Result:

133              lat        lon
662  50.37369  18.889205
134               lat        lon
561  50.448704  19.0...
135               lat        lon
661  50.462271  19.0...
136               lat        lon
559  50.489304  19.0...
137             lat       lon
1  51.474005 -0.450999

You can grab the source data here:

https://github.com/gboeing/2014-summer-travels/tree/master/data