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붓꽃(Iris) 데이터 셋을 이용한 클러스터 평가
from sklearn.preprocessing import scale
from sklearn.datasets import load_iris
from sklearn.cluster import KMeans
# 실루엣 분석 metric 값을 구하기 위한 API 추가
from sklearn.metrics import silhouette_samples, silhouette_score
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
%matplotlib inline
iris = load_iris()
feature_names = ['sepal_length','sepal_width','petal_length','petal_width']
irisDF = pd.DataFrame(data=iris.data, columns=feature_names)
kmeans = KMeans(n_clusters=3, init='k-means++', max_iter=300,random_state=0).fit(irisDF)
irisDF['cluster'] = kmeans.labels_
irisDF.head(3)
sepal_length sepal_width petal_length petal_width cluster
0 5.1 3.5 1.4 0.2 1
1 4.9 3.0 1.4 0.2 1
2 4.7 3.2 1.3 0.2 1
# iris 의 모든 개별 데이터에 실루엣 계수값을 구함.
score_samples = silhouette_samples(iris.data, irisDF['cluster'])
print('silhouette_samples( ) return 값의 shape' , score_samples.shape)
# irisDF에 실루엣 계수 컬럼 추가
irisDF['silhouette_coeff'] = score_samples
# silhouette_samples( ) return 값의 shape (150,)
irisDF.head(20)
sepal_length sepal_width petal_length petal_width cluster silhouette_coeff
0 5.1 3.5 1.4 0.2 1 0.852955
1 4.9 3.0 1.4 0.2 1 0.815495
2 4.7 3.2 1.3 0.2 1 0.829315
3 4.6 3.1 1.5 0.2 1 0.805014
4 5.0 3.6 1.4 0.2 1 0.849302
5 5.4 3.9 1.7 0.4 1 0.748280
6 4.6 3.4 1.4 0.3 1 0.821651
7 5.0 3.4 1.5 0.2 1 0.853905
8 4.4 2.9 1.4 0.2 1 0.752150
9 4.9 3.1 1.5 0.1 1 0.825294
10 5.4 3.7 1.5 0.2 1 0.803103
11 4.8 3.4 1.6 0.2 1 0.835913
12 4.8 3.0 1.4 0.1 1 0.810564
13 4.3 3.0 1.1 0.1 1 0.746150
14 5.8 4.0 1.2 0.2 1 0.702594
15 5.7 4.4 1.5 0.4 1 0.643772
16 5.4 3.9 1.3 0.4 1 0.775684
17 5.1 3.5 1.4 0.3 1 0.851018
18 5.7 3.8 1.7 0.3 1 0.706858
19 5.1 3.8 1.5 0.3 1 0.820301
# 모든 데이터의 평균 실루엣 계수값을 구함.
average_score = silhouette_score(iris.data, irisDF['cluster'])
print('붓꽃 데이터셋 Silhouette Analysis Score:{0:.3f}'.format(average_score))
# 붓꽃 데이터셋 Silhouette Analysis Score:0.553
irisDF['silhouette_coeff'].hist()
irisDF.groupby('cluster')['silhouette_coeff'].mean()
cluster
0 0.451105
1 0.798140
2 0.417320
Name: silhouette_coeff, dtype: float64
클러스터별 평균 실루엣 계수의 시각화를 통한 클러스터 개수 최적화 방법
### 여러개의 클러스터링 갯수를 List로 입력 받아 각각의 실루엣 계수를 면적으로 시각화한 함수 작성
def visualize_silhouette(cluster_lists, X_features):
from sklearn.datasets import make_blobs
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_samples, silhouette_score
import matplotlib.pyplot as plt
import matplotlib.cm as cm
import math
# 입력값으로 클러스터링 갯수들을 리스트로 받아서, 각 갯수별로 클러스터링을 적용하고 실루엣 개수를 구함
n_cols = len(cluster_lists)
# plt.subplots()으로 리스트에 기재된 클러스터링 수만큼의 sub figures를 가지는 axs 생성
fig, axs = plt.subplots(figsize=(4*n_cols, 4), nrows=1, ncols=n_cols)
# 리스트에 기재된 클러스터링 갯수들을 차례로 iteration 수행하면서 실루엣 개수 시각화
for ind, n_cluster in enumerate(cluster_lists):
# KMeans 클러스터링 수행하고, 실루엣 스코어와 개별 데이터의 실루엣 값 계산.
clusterer = KMeans(n_clusters = n_cluster, max_iter=500, random_state=0)
cluster_labels = clusterer.fit_predict(X_features)
sil_avg = silhouette_score(X_features, cluster_labels)
sil_values = silhouette_samples(X_features, cluster_labels)
y_lower = 10
axs[ind].set_title('Number of Cluster : '+ str(n_cluster)+'\n' \
'Silhouette Score :' + str(round(sil_avg,3)) )
axs[ind].set_xlabel("The silhouette coefficient values")
axs[ind].set_ylabel("Cluster label")
axs[ind].set_xlim([-0.1, 1])
axs[ind].set_ylim([0, len(X_features) + (n_cluster + 1) * 10])
axs[ind].set_yticks([]) # Clear the yaxis labels / ticks
axs[ind].set_xticks([0, 0.2, 0.4, 0.6, 0.8, 1])
# 클러스터링 갯수별로 fill_betweenx( )형태의 막대 그래프 표현.
for i in range(n_cluster):
ith_cluster_sil_values = sil_values[cluster_labels==i]
ith_cluster_sil_values.sort()
size_cluster_i = ith_cluster_sil_values.shape[0]
y_upper = y_lower + size_cluster_i
color = cm.nipy_spectral(float(i) / n_cluster)
axs[ind].fill_betweenx(np.arange(y_lower, y_upper), 0, ith_cluster_sil_values, \
facecolor=color, edgecolor=color, alpha=0.7)
axs[ind].text(-0.05, y_lower + 0.5 * size_cluster_i, str(i))
y_lower = y_upper + 10
axs[ind].axvline(x=sil_avg, color="red", linestyle="--")
# make_blobs 을 통해 clustering 을 위한 4개의 클러스터 중심의 500개 2차원 데이터 셋 생성
from sklearn.datasets import make_blobs
X, y = make_blobs(n_samples=500, n_features=2, centers=4, cluster_std=1, \
center_box=(-10.0, 10.0), shuffle=True, random_state=1)
# cluster 개수를 2개, 3개, 4개, 5개 일때의 클러스터별 실루엣 계수 평균값을 시각화
visualize_silhouette([ 2, 3, 4, 5], X)
from sklearn.datasets import load_iris
iris=load_iris()
visualize_silhouette([ 2, 3, 4,5 ], iris.data)
from sklearn.datasets import make_blobs
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_samples, silhouette_score
import matplotlib.pyplot as plt
import matplotlib.cm as cm
import numpy as np
print(__doc__)
# Generating the sample data from make_blobs
# This particular setting has one distinct cluster and 3 clusters placed close
# together.
X, y = make_blobs(n_samples=500,
n_features=2,
centers=4,
cluster_std=1,
center_box=(-10.0, 10.0),
shuffle=True,
random_state=1) # For reproducibility
range_n_clusters = [2, 3, 4, 5, 6]
for n_clusters in range_n_clusters:
# Create a subplot with 1 row and 2 columns
fig, (ax1, ax2) = plt.subplots(1, 2)
fig.set_size_inches(18, 7)
# The 1st subplot is the silhouette plot
# The silhouette coefficient can range from -1, 1 but in this example all
# lie within [-0.1, 1]
ax1.set_xlim([-0.1, 1])
# The (n_clusters+1)*10 is for inserting blank space between silhouette
# plots of individual clusters, to demarcate them clearly.
ax1.set_ylim([0, len(X) + (n_clusters + 1) * 10])
# Initialize the clusterer with n_clusters value and a random generator
# seed of 10 for reproducibility.
clusterer = KMeans(n_clusters=n_clusters, random_state=10)
cluster_labels = clusterer.fit_predict(X)
# The silhouette_score gives the average value for all the samples.
# This gives a perspective into the density and separation of the formed
# clusters
silhouette_avg = silhouette_score(X, cluster_labels)
print("For n_clusters =", n_clusters,
"The average silhouette_score is :", silhouette_avg)
# Compute the silhouette scores for each sample
sample_silhouette_values = silhouette_samples(X, cluster_labels)
y_lower = 10
for i in range(n_clusters):
# Aggregate the silhouette scores for samples belonging to
# cluster i, and sort them
ith_cluster_silhouette_values = \
sample_silhouette_values[cluster_labels == i]
ith_cluster_silhouette_values.sort()
size_cluster_i = ith_cluster_silhouette_values.shape[0]
y_upper = y_lower + size_cluster_i
color = cm.nipy_spectral(float(i) / n_clusters)
ax1.fill_betweenx(np.arange(y_lower, y_upper),
0, ith_cluster_silhouette_values,
facecolor=color, edgecolor=color, alpha=0.7)
# Label the silhouette plots with their cluster numbers at the middle
ax1.text(-0.05, y_lower + 0.5 * size_cluster_i, str(i))
# Compute the new y_lower for next plot
y_lower = y_upper + 10 # 10 for the 0 samples
ax1.set_title("The silhouette plot for the various clusters.")
ax1.set_xlabel("The silhouette coefficient values")
ax1.set_ylabel("Cluster label")
# The vertical line for average silhouette score of all the values
ax1.axvline(x=silhouette_avg, color="red", linestyle="--")
ax1.set_yticks([]) # Clear the yaxis labels / ticks
ax1.set_xticks([-0.1, 0, 0.2, 0.4, 0.6, 0.8, 1])
# 2nd Plot showing the actual clusters formed
colors = cm.nipy_spectral(cluster_labels.astype(float) / n_clusters)
ax2.scatter(X[:, 0], X[:, 1], marker='.', s=30, lw=0, alpha=0.7,
c=colors, edgecolor='k')
# Labeling the clusters
centers = clusterer.cluster_centers_
# Draw white circles at cluster centers
ax2.scatter(centers[:, 0], centers[:, 1], marker='o',
c="white", alpha=1, s=200, edgecolor='k')
for i, c in enumerate(centers):
ax2.scatter(c[0], c[1], marker='$%d$' % i, alpha=1,
s=50, edgecolor='k')
ax2.set_title("The visualization of the clustered data.")
ax2.set_xlabel("Feature space for the 1st feature")
ax2.set_ylabel("Feature space for the 2nd feature")
plt.suptitle(("Silhouette analysis for KMeans clustering on sample data "
"with n_clusters = %d" % n_clusters),
fontsize=14, fontweight='bold')
plt.show()
Automatically created module for IPython interactive environment
For n_clusters = 2 The average silhouette_score is : 0.7049787496083262
For n_clusters = 3 The average silhouette_score is : 0.5882004012129721
For n_clusters = 4 The average silhouette_score is : 0.6505186632729437
For n_clusters = 5 The average silhouette_score is : 0.56376469026194
For n_clusters = 6 The average silhouette_score is : 0.4504666294372765
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