1import numpy as np
2
3def kmeans_xufive(ds, k):
4 '''k-means聚類算法
5
6 k - 指定分簇數(shù)量
7 ds - ndarray(m, n)，m個樣本的數(shù)據(jù)集，每個樣本n個屬性值
8 '''
9
10 m, n = ds.shape # m：樣本數(shù)量，n：每個樣本的屬性值個數(shù)
11 result = np.empty(m, dtype=np.int) # m個樣本的聚類結(jié)果
12 cores = np.empty((k, n)) # k個質(zhì)心
13 cores = ds[np.random.choice(np.arange(m), k, replace=False)] # 從m個數(shù)據(jù)樣本中不重復(fù)地隨機選擇k個樣本作為質(zhì)心
14
15 while True: # 迭代計算
16 d = np.square(np.repeat(ds, k, axis=0).reshape(m, k, n) - cores)
17 distance = np.sqrt(np.sum(d, axis=2)) # ndarray(m, k)，每個樣本距離k個質(zhì)心的距離，共有m行
18 index_min = np.argmin(distance, axis=1) # 每個樣本距離最近的質(zhì)心索引序號
19
20 if (index_min == result).all(): # 如果樣本聚類沒有改變
21 return result, cores # 則返回聚類結(jié)果和質(zhì)心數(shù)據(jù)
22
23 result[:] = index_min # 重新分類
24 for i in range(k): # 遍歷質(zhì)心集
25 items = ds[result==i] # 找出對應(yīng)當(dāng)前質(zhì)心的子樣本集
26 cores[i] = np.mean(items, axis=0) # 以子樣本集的均值作為當(dāng)前質(zhì)心的位置 1import numpy as np
2
3# 加載數(shù)據(jù)
4def loadDataSet(fileName):
5 data = np.loadtxt(fileName,delimiter='\t')
6 return data
7
8# 歐氏距離計算
9def distEclud(x,y):
10 return np.sqrt(np.sum((x-y)**2)) # 計算歐氏距離
11
12# 為給定數(shù)據(jù)集構(gòu)建一個包含K個隨機質(zhì)心的集合
13def randCent(dataSet,k):
14 m,n = dataSet.shape
15 centroids = np.zeros((k,n))
16 for i in range(k):
17 index = int(np.random.uniform(0,m)) #
18 centroids[i,:] = dataSet[index,:]
19 return centroids
20
21# k均值聚類
22def kmeans_open(dataSet,k):
23
24 m = np.shape(dataSet)[0] #行的數(shù)目
25 # 第一列存樣本屬于哪一簇
26 # 第二列存樣本的到簇的中心點的誤差
27 clusterAssment = np.mat(np.zeros((m,2)))
28 clusterChange = True
29
30 # 第1步 初始化centroids
31 centroids = randCent(dataSet,k)
32 while clusterChange:
33 clusterChange = False
34
35 # 遍歷所有的樣本（行數(shù)）
36 for i in range(m):
37 minDist = 100000.0
38 minIndex = -1
39
40 # 遍歷所有的質(zhì)心
41 #第2步 找出最近的質(zhì)心
42 for j in range(k):
43 # 計算該樣本到質(zhì)心的歐式距離
44 distance = distEclud(centroids[j,:],dataSet[i,:])
45 if distance < minDist:
46 minDist = distance
47 minIndex = j
48 # 第 3 步：更新每一行樣本所屬的簇
49 if clusterAssment[i,0] != minIndex:
50 clusterChange = True
51 clusterAssment[i,:] = minIndex,minDist**2
52 #第 4 步：更新質(zhì)心
53 for j in range(k):
54 pointsInCluster = dataSet[np.nonzero(clusterAssment[:,0].A == j)[0]] # 獲取簇類所有的點
55 centroids[j,:] = np.mean(pointsInCluster,axis=0) # 對矩陣的行求均值
56
57 return clusterAssment.A[:,0], centroids 1def create_data_set(*cores):
2 '''生成k-means聚類測試用數(shù)據(jù)集'''
3
4 ds = list()
5 for x0, y0, z0 in cores:
6 x = np.random.normal(x0, 0.1+np.random.random()/3, z0)
7 y = np.random.normal(y0, 0.1+np.random.random()/3, z0)
8 ds.append(np.stack((x,y), axis=1))
9
10 return np.vstack(ds) 1import time
2import matplotlib.pyplot as plt
3
4k = 4
5ds = create_data_set((0,0,2500), (0,2,2500), (2,0,2500), (2,2,2500))
6
7t0 = time.time()
8result, cores = kmeans_xufive(ds, k)
9t = time.time() - t0
10
11plt.scatter(ds[:,0], ds[:,1], s=1, c=result.astype(np.int))
12plt.scatter(cores[:,0], cores[:,1], marker='x', c=np.arange(k))
13plt.show()
14
15print(u'使用kmeans_xufive算法，1萬個樣本點，耗時%f0.3秒'%t)
16
17t0 = time.time()
18result, cores = kmeans_open(ds, k)
19t = time.time() - t0
20
21plt.scatter(ds[:,0], ds[:,1], s=1, c=result.astype(np.int))
22plt.scatter(cores[:,0], cores[:,1], marker='x', c=np.arange(k))
23plt.show()
24
25print(u'使用kmeans_open算法，1萬個樣本點，耗時%f0.3秒'%t)
測試結(jié)果如下：
1PS D:\XufiveGit\CSDN\code> py -3 .\k-means.py
2使用kmeans_xufive算法，1萬個樣本點，耗時0.0156550.3秒
3使用kmeans_open算法，1萬個樣本點，耗時3.9990890.3秒
