X-means
目次
X-means¶
参考文献
Pelleg, Dan, and Andrew W. Moore. "X-means: Extending k-means with efficient estimation of the number of clusters." Icml. Vol. 1. 2000.
# Google Colaboratory で実行する場合はインストールする
if str(get_ipython()).startswith("<google.colab."):
!pip install japanize_matplotlib
import numpy as np
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans
from sklearn.datasets import make_blobs
---------------------------------------------------------------------------
ModuleNotFoundError Traceback (most recent call last)
Input In [2], in <cell line: 2>()
1 import numpy as np
----> 2 import matplotlib.pyplot as plt
4 from sklearn.cluster import KMeans
5 from sklearn.datasets import make_blobs
ModuleNotFoundError: No module named 'matplotlib'
# 表示する文字サイズを調整
plt.rc("font", size=20)
plt.rc("legend", fontsize=16)
plt.rc("xtick", labelsize=14)
plt.rc("ytick", labelsize=14)
# youtube動画を表示
import IPython.display
from IPython.display import Image
np.random.seed(777)
k-meansでkをあらかじめ指定¶
def plot_by_kmeans(X, k=5):
y_pred = KMeans(n_clusters=k, random_state=random_state, init="random").fit_predict(
X
)
plt.scatter(X[:, 0], X[:, 1], c=y_pred, marker="x")
plt.title(f"k-means, n_clusters={k}")
# サンプルデータを作成
n_samples = 1000
random_state = 117117
X, _ = make_blobs(
n_samples=n_samples, random_state=random_state, cluster_std=1, centers=10
)
# k-means++を実行
plot_by_kmeans(X)
x-meanでクラスタ数を指定せずに実行¶
BAYESIAN_INFORMATION_CRITERION¶
from pyclustering.cluster.xmeans import xmeans
from pyclustering.cluster.center_initializer import kmeans_plusplus_initializer
BAYESIAN_INFORMATION_CRITERION = 0
MINIMUM_NOISELESS_DESCRIPTION_LENGTH = 1
def plot_by_xmeans(
X, c_min=3, c_max=10, criterion=BAYESIAN_INFORMATION_CRITERION, tolerance=0.025
):
initial_centers = kmeans_plusplus_initializer(X, c_min).initialize()
xmeans_instance = xmeans(
X, initial_centers, c_max, criterion=criterion, tolerance=tolerance
)
xmeans_instance.process()
# プロット用のデータを作成
clusters = xmeans_instance.get_clusters()
n_samples = X.shape[0]
c = []
for i, cluster_i in enumerate(clusters):
X_ci = X[cluster_i]
color_ci = [i for _ in cluster_i]
plt.scatter(X_ci[:, 0], X_ci[:, 1], marker="x")
plt.title("x-means")
# x-meansを実行
plot_by_xmeans(X, c_min=3, c_max=10, criterion=BAYESIAN_INFORMATION_CRITERION)
MINIMUM_NOISELESS_DESCRIPTION_LENGTH¶
plot_by_xmeans(X, c_min=3, c_max=10, criterion=MINIMUM_NOISELESS_DESCRIPTION_LENGTH)
toleranceの影響¶
X, _ = make_blobs(
n_samples=2000,
random_state=random_state,
cluster_std=0.4,
centers=10,
)
plt.figure(figsize=(25, 5))
for i, ti in enumerate(np.linspace(0.0001, 1, 5)):
ti = np.round(ti, 4)
plt.subplot(1, 10, i + 1)
plot_by_xmeans(
X, c_min=3, c_max=10, criterion=BAYESIAN_INFORMATION_CRITERION, tolerance=ti
)
plt.title(f"tol={ti}")
色々なデータに対して k-means と x-means を比較する¶
for i in range(5):
X, _ = make_blobs(
n_samples=n_samples,
random_state=random_state,
cluster_std=0.7,
centers=5 + i * 5,
)
plt.figure(figsize=(10, 5))
plt.subplot(1, 2, 1)
plot_by_kmeans(X)
plt.subplot(1, 2, 2)
plot_by_xmeans(X, c_min=3, c_max=20)
plt.show()
