在python中用DBSCAN对空间（纬度、经度）数据进行聚类后，可以得到聚类中心点吗？

Question

DBSCAN与k-means或k-medoids相比有很大的不同，后者假设聚类应该具有特定的形状。它假设聚类是一组彼此紧密相连的点，在数据空间中形成一个密集的点的邻域。

我可以计算每个簇的数据点的平均数，得到每个簇的中心点。但这会是一个正确的过程吗。因为中心点的概念似乎只对具有特定形状的簇可行，如超球面。

请回答通过DBSCAN计算聚类的中心点是否正确？

Answer 1

试试这个。

# 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()

结果：

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

你可以在这里获取源数据:

https:/github.comgboeing2014-summer-travelstreemasterdata。