问题描述

我的目标是根据 xy 点的接近度对它们进行聚类。具体来说，将彼此靠近的点进行分组。我也希望使用一个单独的参考点来对数据进行聚类。

注意：我有多组需要独立聚类的数据。例如，使用下面的每个唯一值Item表示一组不同的数据。我可以有多个独特的数据集，它们的稀疏性都不同。因此，任何通过预定数量的集群的技术都是不现实的，因为我每次都必须手动检查拟合并调整适当的参数。

因此，迄今为止最好的方法是某种形式的密度聚类（DBSCAN、OPTICS）。

但是，虽然我将紧密结合在一起的点聚集在一起，但我希望通过一些截止以保持预期的集群球形。另一方面，我不想过多地减少可到达区域，因为我错过了靠近参考点和核心点的点，但是一个小的差距会丢弃我希望包括的点。

下面显示下面的困境。Item 1表示可达性应该如何降低以确保参考品脱周围的聚集点是球形的。虽然Item 2 显示了可到达区域如何需要更高以允许包含密集区域内的点。

我希望我可以调整一个参数或包含一个单独的功能而不是强制它。因为参考点周围的密集区域可能会有所不同，所以我不愿意强制排除特定半径之外的每个点。

import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
from sklearn.cluster import DBSCAN
import seaborn as sns
from sklearn.cluster import OPTICS

fig, ax = plt.subplots(figsize = (6,6))
ax.grid(False)

df = pd.DataFrame({   
    'Item' : [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2],                                
    'x' : [-4.0,-1.0,0.5,0.0,0.0,2.0,3.0,5.0,10.0,-2.0,2.0,5.0,7.5,15.0,0.0,-22.0,-20.0,-20.0,-6.5,20.5,0.0,20.0,-20.0,-15.0,20.0,-15.0,-10.0,-2.0,0.0,3.0,-3.0,-7.0,-7.5,-9.0,-4.0,1.5,-1.0,-5.0,-4.5,-3.7,15.0,-20.0,-22.0,-20.0,-20.0,-12.0,20.5,6.0,20.0,-20.0,-15.0,20.0,-15.0,-10.0],
    'y' : [0.0,1.0,-0.5,0.5,-0.5,0.0,1.0,0.0,0.0,-2.0,-2.0,-7.0,-0.5,-10.5,-7.5,0.0,16.0,-15.0,5.0,13.5,3.0,-20.0,2.0,-17.5,-15,19.0,20.0,4.0,-2.0,0.0,0.0,2.5,2.0,-1.5,5.0,0.0,3.5,2.0,-5.5,-6.5,-10.5,-20.5,0.0,16.0,-15.0,5.0,13.5,6.0,-20.0,2.0,-17.5,-15,19.0,20.0],     
    'X_Ref' : [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0],
    'Y_Ref' : [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0],           
   })

# not spherical
df = df[df['Item'] == 1]

# spherical but reachable area too small
#df = df[df['Item'] == 2]

df['distance'] = np.sqrt((df['X_Ref'] - df['x'])**2 + (df['Y_Ref'] - df['y'])**2)

Y_sklearn = df[['x','y']].values

ax.scatter(df['x'], df['y'], marker = 'o', s = 5)
ax.scatter(df['X_Ref'], df['Y_Ref'], c = 'w', edgecolor = 'k', marker = 'o', s = 7.5, zorder = 2)

#clusterer = DBSCAN(eps = 7.5, min_samples = 3)
#labels_clusters = clusterer.fit_predict(Y_sklearn)

clusterer = OPTICS(min_samples = 2, xi = 0.25, min_cluster_size = 0.25, max_eps = 5)
clusterer.fit(Y_sklearn)
labels_clusters = clusterer.fit_predict(Y_sklearn)

#Add cluster labels as a new column to original DataFrame.
df['cluster'] = labels_clusters
df['cluster'] = df['cluster'].astype('category')

sns.scatterplot(data = df,
            x = 'x',
            y = 'y',
            hue = 'cluster',
            ax = ax,
            legend = 'full',                
            )

第 1 项：半径右侧的点应从核心点中排除

第2项：半径内的点应包含在核心点中

标签： pythoncluster-analysisdbscanoptics-algorithm

解决方案

我相信我们可以重新表述这个问题。我不确定聚类方法是最好的。

通过使用距离聚类

""""
https://stackoverflow.com/questions/66099958/density-clustering-around-a-separate-point-python
"""
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
from sklearn.cluster import DBSCAN
import seaborn as sns
from sklearn.cluster import OPTICS
from sklearn.cluster import MiniBatchKMeans, KMeans
import matplotlib.pyplot as plt

# not spherical
df = pd.DataFrame({
    'x' : [-4.0,-1.0,0.5,0.0,0.0,2.0,3.0,5.0,12.0,-2.0,2.0,8.0,8.5,15.0,-20.0,-22.0,-20.0,-20.0,-10.0,20.5,0.0,20.0,-20.0,-15.0,20.0,-15.0,-10.0],
    'y' : [0.0,1.0,-0.5,0.5,-0.5,0.0,1.0,0.0,0.0,-2.0,-2.0,-8.0,-0.5,-10.5,-20.5,0.0,16.0,-15.0,5.0,13.5,3.0,-20.0,2.0,-17.5,-15,19.0,20.0],
    'X_Ref' : [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0],
    'Y_Ref' : [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0],
       })

# spherical but reachable area too small
df1 = pd.DataFrame({
    'x' : [-2.0,0.0,2.0,-3.0,-7.0,-7.5,-9.0,-4.0,1.5,-1.0,-5.0,-4.5,-3.7,15.0,-20.0,-22.0,-20.0,-20.0,-15.0,20.5,8.0,20.0,-20.0,-15.0,20.0,-15.0,-10.0],
    'y' : [4.0,-2.0,0.0,0.0,2.5,2.0,-2.0,5.0,0.0,3.5,2.0,-5.5,-6.5,-10.5,-20.5,0.0,16.0,-15.0,5.0,13.5,5.0,-20.0,2.0,-17.5,-15,19.0,20.0],
    'X_Ref' : [-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0],
    'Y_Ref' : [-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0],
   })

#Distance calculations
df['distance'] = np.sqrt((df['X_Ref'] - df['x'])**2 + (df['Y_Ref'] - df['y'])**2)
def distance_func(df):
    return np.sqrt((df['X_Ref'] - df['x']) ** 2 + (df['Y_Ref'] - df['y']) ** 2)
df1['distance'] = distance_func(df1)

# Change this for the graphs
df = df1.copy()
Y_sklearn = df['distance'].values.reshape(-1, 1)
fig, ax = plt.subplots(figsize = (6,6))
ax.grid(False)
ax.scatter(df['x'], df['y'], marker = 'o', s = 5)
ax.scatter(df['X_Ref'], df['Y_Ref'], c = 'w', edgecolor = 'k', marker = 'o', s = 7.5, zorder = 2)
clusterer = KMeans(init='k-means++', n_clusters=2, n_init=10)
clusterer.fit(Y_sklearn)
labels_clusters = clusterer.fit_predict(Y_sklearn)

#Add cluster labels as a new column to original DataFrame.
df['cluster'] = labels_clusters
df['cluster'] = df['cluster'].astype('category')

sns.scatterplot(data = df,
            x = 'x',
            y = 'y',
            hue = 'cluster',
            ax = ax,
            legend = 'full',
            )

对于 df：

对于 df1：

通过使用面积的边际增加

如前所述，我相信可以使用边缘区域的概念重新表述问题。我们每次添加的每个点都会以不同的方式增加。

换句话说，对每个点使用肘法。

对于面积计算，我将仅代表距离为 2 的幂。

代码：

""""
https://stackoverflow.com/questions/66099958/density-clustering-around-a-separate-point-python
"""
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
from sklearn.cluster import DBSCAN
import seaborn as sns
from sklearn.cluster import OPTICS
from sklearn.cluster import MiniBatchKMeans, KMeans
import matplotlib.pyplot as plt



# not spherical
df = pd.DataFrame({
    'x' : [-4.0,-1.0,0.5,0.0,0.0,2.0,3.0,5.0,12.0,-2.0,2.0,8.0,8.5,15.0,-20.0,-22.0,-20.0,-20.0,-10.0,20.5,0.0,20.0,-20.0,-15.0,20.0,-15.0,-10.0],
    'y' : [0.0,1.0,-0.5,0.5,-0.5,0.0,1.0,0.0,0.0,-2.0,-2.0,-8.0,-0.5,-10.5,-20.5,0.0,16.0,-15.0,5.0,13.5,3.0,-20.0,2.0,-17.5,-15,19.0,20.0],
    'X_Ref' : [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0],
    'Y_Ref' : [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0],
       })

# spherical but reachable area too small
df1 = pd.DataFrame({
    'x' : [-2.0,0.0,2.0,-3.0,-7.0,-7.5,-9.0,-4.0,1.5,-1.0,-5.0,-4.5,-3.7,15.0,-20.0,-22.0,-20.0,-20.0,-15.0,20.5,8.0,20.0,-20.0,-15.0,20.0,-15.0,-10.0],
    'y' : [4.0,-2.0,0.0,0.0,2.5,2.0,-2.0,5.0,0.0,3.5,2.0,-5.5,-6.5,-10.5,-20.5,0.0,16.0,-15.0,5.0,13.5,5.0,-20.0,2.0,-17.5,-15,19.0,20.0],
    'X_Ref' : [-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0,-4.0],
    'Y_Ref' : [-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0],
   })

df['distance'] = np.sqrt((df['X_Ref'] - df['x'])**2 + (df['Y_Ref'] - df['y'])**2)

def distance_func(df):
    return np.sqrt((df['X_Ref'] - df['x']) ** 2 + (df['Y_Ref'] - df['y']) ** 2)

df1['distance'] = distance_func(df1)

# To shiwtch from one dataset to another.
#df=df1.copy()
df['distance_2'] = df['distance']**2


df.sort_values('distance',inplace=True)
#pd.DataFrame(df['marginal_change'].values).plot()
aux = pd.DataFrame(df['distance_2'].values, columns=['distance ** 2'])
aux.plot()


fig, ax = plt.subplots(figsize = (6,6))
ax.grid(False)
ax.scatter(df['x'], df['y'], marker = 'o', s = 5)
ax.scatter(df['X_Ref'], df['Y_Ref'], c = 'w', edgecolor = 'k', marker = 'o', s = 7.5, zorder = 2)


selected_top=10
labels_clusters = np.zeros(df.shape[0])
labels_clusters[0:selected_top] =1

#Add cluster labels as a new column to original DataFrame.
df['cluster'] = labels_clusters
df['cluster'] = df['cluster'].astype('category')

sns.scatterplot(data = df,
            x = 'x',
            y = 'y',
            hue = 'cluster',
            ax = ax,
            legend = 'full',
            )