Python實現聚類K-means演演算法詳解

# 下面的內容儲存在 melons.txt 中
# 第一列為西瓜的密度；第二列為西瓜的含糖率。我們要把這30個西瓜分為3類
0.697 0.460
0.774 0.376
0.634 0.264
0.608 0.318
0.556 0.215
0.403 0.237
0.481 0.149
0.437 0.211
0.666 0.091
0.243 0.267
0.245 0.057
0.343 0.099
0.639 0.161
0.657 0.198
0.360 0.370
0.593 0.042
0.719 0.103
0.359 0.188
0.339 0.241
0.282 0.257
0.748 0.232
0.714 0.346
0.483 0.312
0.478 0.437
0.525 0.369
0.751 0.489
0.532 0.472
0.473 0.376
0.725 0.445
0.446 0.459

import random
import numpy as np
import matplotlib.pyplot as plt

k = 3 # 要分的簇數
rnd = 0 # 輪次，用於控制迭代次數（見上文）
ROUND_LIMIT = 100 # 輪次的上限
THRESHOLD = 1e-10 # 單輪改變距離的閾值，若改變幅度小於該閾值，演演算法終止
melons = [] # 西瓜的列表
clusters = [] # 簇的列表，clusters[i]表示第i簇包含的西瓜

f = open('melons.txt', 'r')
for line in f:
	# 把字串轉化為numpy中的float64型別
    melons.append(np.array(line.split(' '), dtype = np.string_).astype(np.float64))

# random的sample函數從列表中隨機挑選出k個樣本（不重複）。我們在這裡把這些樣本作為均值向量
mean_vectors = random.sample(melons, k)

# 這個while對應上面演演算法的2-17行
while True:
    rnd += 1 # 輪次增加
    change = 0 # 把改變幅度重置為0

	# 清空對簇的劃分，對應上面演演算法的第3行
    clusters = []
    for i in range(k):
        clusters.append([])
    # 這個for對應上面演演算法的4-8行
    for melon in melons:
    	'''
    	argmin 函數找出容器中最小的下標，在這裡這個目標容器是
    	list(map(lambda vec: np.linalg.norm(melon - vec, ord = 2), mean_vectors)),
    	它表示melon與mean_vectors中所有向量的距離列表。
    	(numpy.linalg.norm計算向量的範數,ord = 2即歐幾里得範數，或模長)
    	'''
        c = np.argmin(
            list(map( lambda vec: np.linalg.norm(melon - vec, ord = 2), mean_vectors))
        )
        clusters[c].append(melon)
	# 這個for對應上面演演算法的9-16行
    for i in range(k):
    	# 求每個簇的新均值向量
        new_vector = np.zeros((1,2))
        for melon in clusters[i]:
            new_vector += melon
        new_vector /= len(clusters[i])

        # 累加改變幅度並更新均值向量
        change += np.linalg.norm(mean_vectors[i] - new_vector, ord = 2)
        mean_vectors[i] = new_vector
	# 若超過設定的輪次或者變化幅度<預先設定的閾值，結束演演算法
    if rnd > ROUND_LIMIT or change < THRESHOLD:
        break
print('最終迭代%d輪'%rnd)

colors = ['red', 'green', 'blue']

# 每個簇換一下顏色，同時迭代簇和顏色兩個列表
for i, col in zip(range(k), colors):
    for melon in clusters[i]:
    	# 繪製散點圖
        plt.scatter(melon[0], melon[1], color = col)
plt.show()

import random
import numpy as np
import matplotlib.pyplot as plt

k = 3
rnd = 0
ROUND_LIMIT = 10
THRESHOLD = 1e-10
melons = []
clusters = []
f = open('melons.txt', 'r')
for line in f:
    melons.append(np.array(line.split(' '), dtype = np.string_).astype(np.float64))
mean_vectors = random.sample(melons, k)

while True:
    rnd += 1
    change = 0
    clusters = []
    for i in range(k):
        clusters.append([])
    for melon in melons:
        c = np.argmin(
            list(map( lambda vec: np.linalg.norm(melon - vec, ord = 2), mean_vectors))
        )
        clusters[c].append(melon)
    for i in range(k):
        new_vector = np.zeros((1,2))
        for melon in clusters[i]:
            new_vector += melon
        new_vector /= len(clusters[i])

        change += np.linalg.norm(mean_vectors[i] - new_vector, ord = 2)
        mean_vectors[i] = new_vector

    if rnd > ROUND_LIMIT or change < THRESHOLD:
        break
print('最終迭代%d輪'%rnd)
colors = ['red', 'green', 'blue']
for i, col in zip(range(k), colors):
    for melon in clusters[i]:
        plt.scatter(melon[0], melon[1], color = col)
plt.show()

>>> from sklearn.cluster import KMeans
>>> import numpy as np
>>> X = np.array([[1, 2], [1, 4], [1, 0],
...               [10, 2], [10, 4], [10, 0]])
>>> kmeans = KMeans(n_clusters=2, random_state=0).fit(X)
>>> kmeans.labels_
array([1, 1, 1, 0, 0, 0], dtype=int32)
>>> kmeans.predict([[0, 0], [12, 3]])
array([1, 0], dtype=int32)
>>> kmeans.cluster_centers_
array([[10.,  2.],
       [ 1.,  2.]])

import numpy as np
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans

X = []
f = open('melons.txt', 'r')
for line in f:
    X.append(np.array(line.split(' '), dtype = np.string_).astype(np.float64))
kmeans = KMeans(n_clusters = 3, random_state = 0).fit(X)
colors = ['red', 'green', 'blue']
for i, cluster in enumerate(kmeans.labels_):
    plt.scatter(X[i][0], X[i][1], color = colors[cluster])
plt.show()