聚类算法实践

• Kmeans与Dbscan算法
• 半监督问题解决方案
• 聚类评估方法

# -*- coding: utf-8 -*-
"""
Created on Sat Apr 20 20:42:57 2024

@author: Tom
"""

import numpy as np
import os
# %matplotlib inline
import matplotlib
import matplotlib.pyplot as plt
plt.rcParams["axes.labelsize"] = 14
plt.rcParams["xtick.labelsize"] = 12
plt.rcParams["ytick.labelsize"] = 12
import warnings
warnings.filterwarnings("ignore")
np.random.seed(42)

# Kmeans
from sklearn.datasets import make_blobs

# 指定5个中心点
blob_centers = np.array(
    [[0.2,2.3],
     [-1.5,2.3],
     [-2.8,1.8],
     [-2.8,2.8],
     [-2.8,1.3]])


blob_std = np.array([0.4,0.3,0.1,0.1,0.1])

X,y = make_blobs(n_samples=2000,centers = blob_centers,
                 cluster_std=blob_std,random_state=7)

def plot_clusters(X,y = None):
    plt.scatter(X[:,0], X[:,1], c = y,s = 1)
    plt.xlabel("$x_1$",fontsize = 14)
    plt.ylabel("$x_2$",fontsize = 14,rotation = 0)
plt.figure(figsize=(8,4))

plot_clusters(X)

plt.show()


from sklearn.cluster import KMeans

k = 5

kmeans = KMeans(n_clusters=k,random_state = 45)

# fit_predict(X)与kmeans.labels_ 得到预测结果是一致的
y_pred = kmeans.fit_predict(X)

print(y_pred)

print(kmeans.labels_)

# 得到中心点
print(kmeans.cluster_centers_)


X_new = np.array([[0,2],[3,2],[-3,3],[-3,2.5]])

print(kmeans.predict(X_new))

print(kmeans.transform(X_new))

# 输出每一个样本到各个簇中心点的距离
print(kmeans.transform(X_new))


def plot_data(X):
    plt.plot(X[:,0],X[:,1],"k.",markersize = 2)
    
def plot_centroids(centroids,weights = None,circle_color = "w",cross_color = "k"):
    if weights is not None:
        centroids = centroids[weights > weights.max() / 10]
    plt.scatter(centroids[:,0],centroids[:,1],
                marker = "o",s = 30,linewidths = 8,
                color = circle_color,zorder = 10,alpha = 0.9)
    
    plt.scatter(centroids[:,0],centroids[:,1],
                marker = "x",s = 2,linewidths = 12,
                color = cross_color,zorder = 11,alpha = 1)
    
    

def plot_decision_boundaries(clusterer,X,resolution = 1000,show_centroids = True,
                             show_xlabels = True,show_ylabels = True):
    mins = X.min(axis = 0) - 0.1
    maxs = X.max(axis = 0) + 0.1
    xx,yy = np.meshgrid(np.linspace(mins[0], maxs[0],resolution),
                        np.linspace(mins[1], maxs[1],resolution))
    
    Z = clusterer.predict(np.c_[xx.ravel(),yy.ravel()])
    
    Z = Z.reshape(xx.shape)
    
    plt.contourf(Z,extent = (mins[0],maxs[0],mins[1],maxs[1]),cmap = "Pastel2")
    
    plt.contour(Z,extent = (mins[0],maxs[0],mins[1],maxs[1]),
                linewidths = 1,colors = "k")
    
    plot_data(X)
    
    if show_centroids:
        plot_centroids(clusterer.cluster_centers_)
        
    if show_xlabels:
        plt.xlabel("$x_1$",fontsize = 14)
    else:
        plt.tick_params(labelbottom = "off")
    if show_ylabels:
        plt.ylabel("x_2",fontsize = 14,rotation = 0)
    else:
        plt.tick_params(labelleft = "off")


plt.figure(figsize = (8,4))

plot_decision_boundaries(kmeans, X) 

plt.show()

运行结果:

建模流程解读

# -*- coding: utf-8 -*-
"""
Created on Sat Apr 20 20:42:57 2024

@author: Tom
"""

import numpy as np
import os
# %matplotlib inline
import matplotlib
import matplotlib.pyplot as plt
plt.rcParams["axes.labelsize"] = 14
plt.rcParams["xtick.labelsize"] = 12
plt.rcParams["ytick.labelsize"] = 12
import warnings
warnings.filterwarnings("ignore")
np.random.seed(42)

# Kmeans
from sklearn.datasets import make_blobs

# 指定5个中心点
blob_centers = np.array(
    [[0.2,2.3],
     [-1.5,2.3],
     [-2.8,1.8],
     [-2.8,2.8],
     [-2.8,1.3]])


blob_std = np.array([0.4,0.3,0.1,0.1,0.1])

X,y = make_blobs(n_samples=2000,centers = blob_centers,
                 cluster_std=blob_std,random_state=7)

def plot_clusters(X,y = None):
    plt.scatter(X[:,0], X[:,1], c = y,s = 1)
    plt.xlabel("$x_1$",fontsize = 14)
    plt.ylabel("$x_2$",fontsize = 14,rotation = 0)
plt.figure(figsize=(8,4))

plot_clusters(X)

plt.show()


from sklearn.cluster import KMeans

k = 5

kmeans = KMeans(n_clusters=k,random_state = 45)

# fit_predict(X)与kmeans.labels_ 得到预测结果是一致的
y_pred = kmeans.fit_predict(X)

print(y_pred)

print(kmeans.labels_)

# 得到中心点
print(kmeans.cluster_centers_)


X_new = np.array([[0,2],[3,2],[-3,3],[-3,2.5]])

print(kmeans.predict(X_new))

print(kmeans.transform(X_new))

# 输出每一个样本到各个簇中心点的距离
print(kmeans.transform(X_new))


def plot_data(X):
    plt.plot(X[:,0],X[:,1],"k.",markersize = 2)
    
def plot_centroids(centroids,weights = None,circle_color = "w",cross_color = "k"):
    if weights is not None:
        centroids = centroids[weights > weights.max() / 10]
    plt.scatter(centroids[:,0],centroids[:,1],
                marker = "o",s = 30,linewidths = 8,
                color = circle_color,zorder = 10,alpha = 0.9)
    
    plt.scatter(centroids[:,0],centroids[:,1],
                marker = "x",s = 2,linewidths = 12,
                color = cross_color,zorder = 11,alpha = 1)
    
    

def plot_decision_boundaries(clusterer,X,resolution = 1000,show_centroids = True,
                             show_xlabels = True,show_ylabels = True):
    mins = X.min(axis = 0) - 0.1
    maxs = X.max(axis = 0) + 0.1
    xx,yy = np.meshgrid(np.linspace(mins[0], maxs[0],resolution),
                        np.linspace(mins[1], maxs[1],resolution))
    
    Z = clusterer.predict(np.c_[xx.ravel(),yy.ravel()])
    
    Z = Z.reshape(xx.shape)
    
    plt.contourf(Z,extent = (mins[0],maxs[0],mins[1],maxs[1]),cmap = "Pastel2")
    
    plt.contour(Z,extent = (mins[0],maxs[0],mins[1],maxs[1]),
                linewidths = 1,colors = "k")
    
    plot_data(X)
    
    if show_centroids:
        plot_centroids(clusterer.cluster_centers_)
        
    if show_xlabels:
        plt.xlabel("$x_1$",fontsize = 14)
    else:
        plt.tick_params(labelbottom = "off")
    if show_ylabels:
        plt.ylabel("x_2",fontsize = 14,rotation = 0)
    else:
        plt.tick_params(labelleft = "off")


plt.figure(figsize = (8,4))

plot_decision_boundaries(kmeans, X) 

plt.show()


kmeans_iter1 = KMeans(n_clusters = 5,init = "random",n_init= 1,max_iter = 1,random_state= 1)
kmeans_iter2 = KMeans(n_clusters = 5,init = "random",n_init= 1,max_iter = 2,random_state= 1)
kmeans_iter3 = KMeans(n_clusters = 5,init = "random",n_init= 1,max_iter = 3,random_state= 1)


kmeans_iter1.fit(X)
kmeans_iter2.fit(X)
kmeans_iter3.fit(X)

plt.figure(figsize=(12,8))


plt.subplot(321)

plot_data(X)

plot_centroids(kmeans_iter1.cluster_centers_,circle_color = "r",cross_color = "k")

plt.title("Update cluster_centers")

plt.subplot(322)

plot_decision_boundaries(kmeans_iter1, X,show_xlabels=False,show_ylabels=False)

plt.title("Label")


plt.subplot(323)

plot_decision_boundaries(kmeans_iter1, X,show_xlabels=False,show_ylabels=False)
plot_centroids(kmeans_iter2.cluster_centers_)

plt.title("Update cluster_centers")


plt.subplot(324)

plot_decision_boundaries(kmeans_iter2, X,show_xlabels=False,show_ylabels=False)



plt.subplot(325)

plot_decision_boundaries(kmeans_iter2, X,show_xlabels=False,show_ylabels=False)
plot_centroids(kmeans_iter3.cluster_centers_)

plt.subplot(326)

plot_decision_boundaries(kmeans_iter3, X,show_xlabels=False,show_ylabels=False)


plt.show()

运行结果:

不稳定结果

# -*- coding: utf-8 -*-
"""
Created on Sat Apr 20 20:42:57 2024

@author: Tom
"""

import numpy as np
import os
# %matplotlib inline
import matplotlib
import matplotlib.pyplot as plt
plt.rcParams["axes.labelsize"] = 14
plt.rcParams["xtick.labelsize"] = 12
plt.rcParams["ytick.labelsize"] = 12
import warnings
warnings.filterwarnings("ignore")
np.random.seed(42)

# Kmeans
from sklearn.datasets import make_blobs

# 指定5个中心点
blob_centers = np.array(
    [[0.2,2.3],
     [-1.5,2.3],
     [-2.8,1.8],
     [-2.8,2.8],
     [-2.8,1.3]])


blob_std = np.array([0.4,0.3,0.1,0.1,0.1])

X,y = make_blobs(n_samples=2000,centers = blob_centers,
                 cluster_std=blob_std,random_state=7)

def plot_clusters(X,y = None):
    plt.scatter(X[:,0], X[:,1], c = y,s = 1)
    plt.xlabel("$x_1$",fontsize = 14)
    plt.ylabel("$x_2$",fontsize = 14,rotation = 0)
plt.figure(figsize=(8,4))

plot_clusters(X)

plt.show()


from sklearn.cluster import KMeans

k = 5

kmeans = KMeans(n_clusters=k,random_state = 45)

# fit_predict(X)与kmeans.labels_ 得到预测结果是一致的
y_pred = kmeans.fit_predict(X)

print(y_pred)

print(kmeans.labels_)

# 得到中心点
print(kmeans.cluster_centers_)


X_new = np.array([[0,2],[3,2],[-3,3],[-3,2.5]])

print(kmeans.predict(X_new))

print(kmeans.transform(X_new))

# 输出每一个样本到各个簇中心点的距离
print(kmeans.transform(X_new))


def plot_data(X):
    plt.plot(X[:,0],X[:,1],"k.",markersize = 2)
    
def plot_centroids(centroids,weights = None,circle_color = "w",cross_color = "k"):
    if weights is not None:
        centroids = centroids[weights > weights.max() / 10]
    plt.scatter(centroids[:,0],centroids[:,1],
                marker = "o",s = 30,linewidths = 8,
                color = circle_color,zorder = 10,alpha = 0.9)
    
    plt.scatter(centroids[:,0],centroids[:,1],
                marker = "x",s = 2,linewidths = 12,
                color = cross_color,zorder = 11,alpha = 1)
    
    

def plot_decision_boundaries(clusterer,X,resolution = 1000,show_centroids = True,
                             show_xlabels = True,show_ylabels = True):
    mins = X.min(axis = 0) - 0.1
    maxs = X.max(axis = 0) + 0.1
    xx,yy = np.meshgrid(np.linspace(mins[0], maxs[0],resolution),
                        np.linspace(mins[1], maxs[1],resolution))
    
    Z = clusterer.predict(np.c_[xx.ravel(),yy.ravel()])
    
    Z = Z.reshape(xx.shape)
    
    plt.contourf(Z,extent = (mins[0],maxs[0],mins[1],maxs[1]),cmap = "Pastel2")
    
    plt.contour(Z,extent = (mins[0],maxs[0],mins[1],maxs[1]),
                linewidths = 1,colors = "k")
    
    plot_data(X)
    
    if show_centroids:
        plot_centroids(clusterer.cluster_centers_)
        
    if show_xlabels:
        plt.xlabel("$x_1$",fontsize = 14)
    else:
        plt.tick_params(labelbottom = "off")
    if show_ylabels:
        plt.ylabel("x_2",fontsize = 14,rotation = 0)
    else:
        plt.tick_params(labelleft = "off")


plt.figure(figsize = (8,4))

plot_decision_boundaries(kmeans, X) 

plt.show()


kmeans_iter1 = KMeans(n_clusters = 5,init = "random",n_init= 1,max_iter = 1,random_state= 1)
kmeans_iter2 = KMeans(n_clusters = 5,init = "random",n_init= 1,max_iter = 2,random_state= 1)
kmeans_iter3 = KMeans(n_clusters = 5,init = "random",n_init= 1,max_iter = 3,random_state= 1)


kmeans_iter1.fit(X)
kmeans_iter2.fit(X)
kmeans_iter3.fit(X)

plt.figure(figsize=(12,8))


plt.subplot(321)

plot_data(X)

plot_centroids(kmeans_iter1.cluster_centers_,circle_color = "r",cross_color = "k")

plt.title("Update cluster_centers")

plt.subplot(322)

plot_decision_boundaries(kmeans_iter1, X,show_xlabels=False,show_ylabels=False)

plt.title("Label")


plt.subplot(323)

plot_decision_boundaries(kmeans_iter1, X,show_xlabels=False,show_ylabels=False)
plot_centroids(kmeans_iter2.cluster_centers_)

plt.title("Update cluster_centers")


plt.subplot(324)

plot_decision_boundaries(kmeans_iter2, X,show_xlabels=False,show_ylabels=False)



plt.subplot(325)

plot_decision_boundaries(kmeans_iter2, X,show_xlabels=False,show_ylabels=False)
plot_centroids(kmeans_iter3.cluster_centers_)

plt.subplot(326)

plot_decision_boundaries(kmeans_iter3, X,show_xlabels=False,show_ylabels=False)


plt.show()



def plot_clusterer_comparison(c1,c2,X):
    c1.fit(X)
    c2.fit(X)
    
    plt.figure(figsize=(12,4))
    
    plt.subplot(121)
    
    plot_decision_boundaries(c1, X)
    
    plt.subplot(122)
    
    plot_decision_boundaries(c2, X)
    
c1 = KMeans(n_clusters=5,init = "random",n_init = 1,random_state=15)

c2 = KMeans(n_clusters=5,init = "random",n_init = 1,random_state=19)

plot_clusterer_comparison(c1, c2, X)

运行结果:

评估指标Inertia

• Inertia指标：每个样本与其质心的距离

# -*- coding: utf-8 -*-
"""
Created on Sat Apr 20 20:42:57 2024

@author: Tom
"""

import numpy as np
import os
# %matplotlib inline
import matplotlib
import matplotlib.pyplot as plt
plt.rcParams["axes.labelsize"] = 14
plt.rcParams["xtick.labelsize"] = 12
plt.rcParams["ytick.labelsize"] = 12
import warnings
warnings.filterwarnings("ignore")
np.random.seed(42)

# Kmeans
from sklearn.datasets import make_blobs

# 指定5个中心点
blob_centers = np.array(
    [[0.2,2.3],
     [-1.5,2.3],
     [-2.8,1.8],
     [-2.8,2.8],
     [-2.8,1.3]])


blob_std = np.array([0.4,0.3,0.1,0.1,0.1])

X,y = make_blobs(n_samples=2000,centers = blob_centers,
                 cluster_std=blob_std,random_state=7)

def plot_clusters(X,y = None):
    plt.scatter(X[:,0], X[:,1], c = y,s = 1)
    plt.xlabel("$x_1$",fontsize = 14)
    plt.ylabel("$x_2$",fontsize = 14,rotation = 0)
plt.figure(figsize=(8,4))

plot_clusters(X)

plt.show()


from sklearn.cluster import KMeans

k = 5

kmeans = KMeans(n_clusters=k,random_state = 45)

# fit_predict(X)与kmeans.labels_ 得到预测结果是一致的
y_pred = kmeans.fit_predict(X)

print(y_pred)

print(kmeans.labels_)

# 得到中心点
print(kmeans.cluster_centers_)


X_new = np.array([[0,2],[3,2],[-3,3],[-3,2.5]])

print(kmeans.predict(X_new))

print(kmeans.transform(X_new))

# 输出每一个样本到各个簇中心点的距离
print(kmeans.transform(X_new))


def plot_data(X):
    plt.plot(X[:,0],X[:,1],"k.",markersize = 2)
    
def plot_centroids(centroids,weights = None,circle_color = "w",cross_color = "k"):
    if weights is not None:
        centroids = centroids[weights > weights.max() / 10]
    plt.scatter(centroids[:,0],centroids[:,1],
                marker = "o",s = 30,linewidths = 8,
                color = circle_color,zorder = 10,alpha = 0.9)
    
    plt.scatter(centroids[:,0],centroids[:,1],
                marker = "x",s = 2,linewidths = 12,
                color = cross_color,zorder = 11,alpha = 1)
    
    

def plot_decision_boundaries(clusterer,X,resolution = 1000,show_centroids = True,
                             show_xlabels = True,show_ylabels = True):
    mins = X.min(axis = 0) - 0.1
    maxs = X.max(axis = 0) + 0.1
    xx,yy = np.meshgrid(np.linspace(mins[0], maxs[0],resolution),
                        np.linspace(mins[1], maxs[1],resolution))
    
    Z = clusterer.predict(np.c_[xx.ravel(),yy.ravel()])
    
    Z = Z.reshape(xx.shape)
    
    plt.contourf(Z,extent = (mins[0],maxs[0],mins[1],maxs[1]),cmap = "Pastel2")
    
    plt.contour(Z,extent = (mins[0],maxs[0],mins[1],maxs[1]),
                linewidths = 1,colors = "k")
    
    plot_data(X)
    
    if show_centroids:
        plot_centroids(clusterer.cluster_centers_)
        
    if show_xlabels:
        plt.xlabel("$x_1$",fontsize = 14)
    else:
        plt.tick_params(labelbottom = "off")
    if show_ylabels:
        plt.ylabel("x_2",fontsize = 14,rotation = 0)
    else:
        plt.tick_params(labelleft = "off")


"""

plt.figure(figsize = (8,4))

plot_decision_boundaries(kmeans, X) 

plt.show()


kmeans_iter1 = KMeans(n_clusters = 5,init = "random",n_init= 1,max_iter = 1,random_state= 1)
kmeans_iter2 = KMeans(n_clusters = 5,init = "random",n_init= 1,max_iter = 2,random_state= 1)
kmeans_iter3 = KMeans(n_clusters = 5,init = "random",n_init= 1,max_iter = 3,random_state= 1)


kmeans_iter1.fit(X)
kmeans_iter2.fit(X)
kmeans_iter3.fit(X)

plt.figure(figsize=(12,8))


plt.subplot(321)

plot_data(X)

plot_centroids(kmeans_iter1.cluster_centers_,circle_color = "r",cross_color = "k")

plt.title("Update cluster_centers")

plt.subplot(322)

plot_decision_boundaries(kmeans_iter1, X,show_xlabels=False,show_ylabels=False)

plt.title("Label")


plt.subplot(323)

plot_decision_boundaries(kmeans_iter1, X,show_xlabels=False,show_ylabels=False)
plot_centroids(kmeans_iter2.cluster_centers_)

plt.title("Update cluster_centers")


plt.subplot(324)

plot_decision_boundaries(kmeans_iter2, X,show_xlabels=False,show_ylabels=False)



plt.subplot(325)

plot_decision_boundaries(kmeans_iter2, X,show_xlabels=False,show_ylabels=False)
plot_centroids(kmeans_iter3.cluster_centers_)

plt.subplot(326)

plot_decision_boundaries(kmeans_iter3, X,show_xlabels=False,show_ylabels=False)


plt.show()

"""



def plot_clusterer_comparison(c1,c2,X):
    c1.fit(X)
    c2.fit(X)
    
    plt.figure(figsize=(12,4))
    
    plt.subplot(121)
    
    plot_decision_boundaries(c1, X)
    
    plt.subplot(122)
    
    plot_decision_boundaries(c2, X)
    
c1 = KMeans(n_clusters=5,init = "random",n_init = 1,random_state=15)

c2 = KMeans(n_clusters=5,init = "random",n_init = 1,random_state=19)

plot_clusterer_comparison(c1, c2, X)




print("-----------------------------------------------")

# Inertia指标：每个样本与其质心的距离

print(kmeans.inertia_)

print(kmeans.transform(X))

print(kmeans.labels_)

X_dist = kmeans.transform(X)


print(X_dist[np.arange(len(X_dist)),kmeans.labels_])

# 等于Inertia
print(np.sum(X_dist[np.arange(len(X_dist)),kmeans.labels_] ** 2))

print(kmeans.score(X))


print(c1.inertia_)

print(c2.inertia_)

运行结果: