三大指标助力K均值与层次聚类数选定及Python示例代码

# Libraries to help with reading and manipulating data
import pandas as pd
import numpy as np
# libaries to help with data visualization
import matplotlib.pyplot as plt
import seaborn as sns
# Removes the limit for the number of displayed columns
pd.set_option("display.max_columns", None)
# Sets the limit for the number of displayed rows
pd.set_option("display.max_rows", 200)
# to scale the data using z-score
from sklearn.preprocessing import StandardScaler
# to compute distances
from scipy.spatial.distance import cdist, pdist
# to perform k-means clustering and compute silhouette scores
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score
# to visualize the elbow curve and silhouette scores
from yellowbrick.cluster import KElbowVisualizer, SilhouetteVisualizer
# to perform hierarchical clustering, compute cophenetic correlation, and create dendrograms
from sklearn.cluster import AgglomerativeClustering
from scipy.cluster.hierarchy import dendrogram, linkage, cophenet
sns.set(color_codes=True)


from sklearn.datasets import load_iris, load_wine, load_digits, make_blobs
wine = load_wine()
X_wine = wine.data
X_wine

scaler=StandardScaler()
X_wine_int=X_wine.copy()
X_wine_interim=scaler.fit_transform(X_wine_int)
X_wine_scaled=pd.DataFrame(X_wine_interim)
X_wine_scaled.head(10)

from gap_statistic import OptimalK
from sklearn.cluster import KMeans
def KMeans_clustering_func(X, k):
    """ 
    K Means Clustering function, which uses the K Means model from sklearn.
    These user-defined functions *must* take the X (input features) and a k 
    when initializing OptimalK
    """
    
    # Include any clustering Algorithm that can return cluster centers
    
    m = KMeans(random_state=11, n_clusters=k)
    m.fit(X)
    return m.cluster_centers_, m.predict(X)
#--------------------create a wrapper around OptimalK to extract cluster centers and cluster labels
optimalK = OptimalK(clusterer=KMeans_clustering_func)
#--------------------Run optimal K on the input data (subset_scaled_interim) and number of clusters
n_clusters = optimalK(X_wine_scaled, cluster_array=np.arange(1, 15))
print('Optimal clusters: ', n_clusters)
#--------------------Gap Statistics data frame
optimalK.gap_df[['n_clusters', 'gap_value']]

plt.figure(figsize=(10,6))
n_clusters=3
plt.plot(optimalK.gap_df.n_clusters.values, optimalK.gap_df.gap_value.values, linewidth=2)
plt.scatter(optimalK.gap_df[optimalK.gap_df.n_clusters == n_clusters].n_clusters,
            optimalK.gap_df[optimalK.gap_df.n_clusters == n_clusters].gap_value, s=250, c='r')
plt.grid(True)
plt.xlabel('Cluster Count')
plt.ylabel('Gap Value')
plt.title('Gap Values by Cluster Count')
plt.axvline(3, linestyle="--")
plt.show()

plt.figure(figsize=(10,6))
model = KMeans(random_state=1)
# k is a range of the number of clusters.
visualizer = KElbowVisualizer(
    model, k=(2, 10), metric="calinski_harabasz", timings=True
)
visualizer.fit(X_wine_scaled)  # Fit the data to the visualizer
visualizer.show()  # Finalize and generate the plot

from sklearn.metrics import davies_bouldin_score
def get_Hmeans_score(  data, distance, link, center):  
    """
    returns the  score regarding Davies Bouldin for points to centers
    INPUT:
        data - the dataset you want to fit Agglomerative to
        distance - the distance for AgglomerativeClustering
        link - the linkage method for AgglomerativeClustering
        center - the number of clusters you want (the k value)
    OUTPUT:
        score - the Davies Bouldin score for the Hierarchical model fit to the data
    """
    hmeans = AgglomerativeClustering(n_clusters=center,linkage=link)
    model = hmeans.fit_predict(data)
    score = davies_bouldin_score(data, model)
    return score


centers = list(range(2, 10)) #------Number of Clusters in the data
avg_scores = []
for center in centers:
  avg_scores.append(get_Hmeans_score(X_wine_scaled, "euclidean", "average", center))
plt.figure(figsize=(15,6));
 
plt.plot(centers, avg_scores, linestyle="-", marker="o", color="b")
plt.xlabel("K")
plt.ylabel("Davies Bouldin score")
plt.title("Davies Bouldin score vs. K")

plt.figure(figsize=(10,6))
model = KMeans(random_state=1)
# k is a range of the number of clusters.
visualizer = KElbowVisualizer(
    model, k=(2, 10), metric="silhouette", timings=True
)
visualizer.fit(X_wine_scaled)  # Fit the data to the visualizer
visualizer.show()  # Finalize and generate the plot