一位读者建议多分享一些具体算法相关的内容,这期分享一下数据挖掘相关的算法。
简介
又叫K-均值算法,是非监督学习中的聚类算法。
基本思想
k-means算法比较简单。在k-means算法中,用cluster来表示簇;容易证明k-means算法收敛等同于所有质心不再发生变化。基本的k-means算法流程如下:
选取k个初始质心(作为初始cluster,每个初始cluster只包含一个点);
repeat:
对每个样本点,计算得到距其最近的质心,将其类别标为该质心所对应的cluster;
重新计算k个cluster对应的质心(质心是cluster中样本点的均值);
until 质心不再发生变化
repeat的次数决定了算法的迭代次数。实际上,k-means的本质是最小化目标函数,目标函数为每个点到其簇质心的距离的平方和:
N是元素个数,x表示元素,c(j)表示第j簇的质心
算法复杂度
时间复杂度是O(nkt) ,其中n代表元素个数,t代表算法迭代的次数,k代表簇的数目
优缺点
优点
简单、快速;
对大数据集有较高的效率并且是可伸缩性的;
时间复杂度近于线性,适合挖掘大规模数据集。
缺点
k-means是局部最优,因而对初始质心的选取敏感;
选择能达到目标函数最优的k值是非常困难的。
代码
# coding:utf-8
import numpy as np
import matplotlib.pyplot as plt
def loadDataSet(fileName):
'''
加载测试数据集,返回一个列表,列表的元素是一个坐标
'''
dataList = []
with open(fileName) as fr:
for line in fr.readlines():
curLine = line.strip().split('\t')
fltLine = list(map(float, curLine))
dataList.append(fltLine)
return dataList
def randCent(dataSet, k):
'''
随机生成k个初始的质心
'''
n = np.shape(dataSet)[1] # n表示数据集的维度
centroids = np.mat(np.zeros((k, n)))
for j in range(n):
minJ = min(dataSet[:, j])
rangeJ = float(max(dataSet[:, j]) - minJ)
centroids[:, j] = np.mat(minJ + rangeJ * np.random.rand(k, 1))
return centroids
def kMeans(dataSet, k):
'''
KMeans算法,返回最终的质心坐标和每个点所在的簇
'''
m = np.shape(dataSet)[0] # m表示数据集的长度(个数)
clusterAssment = np.mat(np.zeros((m, 2)))
centroids = randCent(dataSet, k) # 保存k个初始质心的坐标
clusterChanged = True
iterIndex = 1 # 迭代次数
while clusterChanged:
clusterChanged = False
for i in range(m):
minDist = np.inf
minIndex = -1
for j in range(k):
distJI = np.linalg.norm(np.array(centroids[j, :]) - np.array(dataSet[i, :]))
if distJI < minDist:
minDist = distJI
minIndex = j
if clusterAssment[i, 0] != minIndex: clusterChanged = True
clusterAssment[i, :] = minIndex, minDist ** 2
print("第%d次迭代后%d个质心的坐标:\n%s" % (iterIndex, k, centroids)) # 第一次迭代的质心坐标就是初始的质心坐标
iterIndex += 1
for cent in range(k):
ptsInClust = dataSet[np.nonzero(clusterAssment[:, 0].A == cent)[0]] # get all the point in this cluster
centroids[cent, :] = np.mean(ptsInClust, axis=0)
return centroids, clusterAssment
def showCluster(dataSet, k, centroids, clusterAssment):
'''
数据可视化,只能画二维的图(若是三维的坐标图则直接返回1)
'''
numSamples, dim = dataSet.shape
if dim != 2:
return 1
mark = ['or', 'ob', 'og', 'ok', 'oy', 'om', 'oc', '^r', '+r', 'sr', 'dr', '<r', 'pr']
# draw all samples
for i in range(numSamples):
markIndex = int(clusterAssment[i, 0])
plt.plot(dataSet[i, 0], dataSet[i, 1], mark[markIndex])
mark = ['Pr', 'Pb', 'Pg', 'Pk', 'Py', 'Pm', 'Pc', '^b', '+b', 'sb', 'db', '<b', 'pb']
# draw the centroids
for i in range(k):
plt.plot(centroids[i, 0], centroids[i, 1], mark[i], markersize=12)
plt.show()
if __name__ == '__main__':
dataMat = np.mat(loadDataSet('./data.txt')) # mat是numpy中的函数,将列表转化成矩阵
k = 6 # 选定k值,也就是簇的个数(可以指定为其他数)
cent, clust = kMeans(dataMat, k)
showCluster(dataMat, k, cent, clust)
txt内容为:
1.658985 4.285136
-3.453687 3.424321
4.838138 -1.151539
-5.379713 -3.362104
0.972564 2.924086
-3.567919 1.531611
0.450614 -3.302219
-3.487105 -1.724432
2.668759 1.594842
-3.156485 3.191137
3.165506 -3.999838
-2.786837 -3.099354
4.208187 2.984927
-2.123337 2.943366
0.704199 -0.479481
-0.392370 -3.963704
2.831667 1.574018
-0.790153 3.343144
2.943496 -3.357075
-3.195883 -2.283926
2.336445 2.875106
-1.786345 2.554248
2.190101 -1.906020
-3.403367 -2.778288
1.778124 3.880832
-1.688346 2.230267
2.592976 -2.054368
-4.007257 -3.207066
2.257734 3.387564
-2.679011 0.785119
0.939512 -4.023563
-3.674424 -2.261084
2.046259 2.735279
-3.189470 1.780269
4.372646 -0.822248
-2.579316 -3.497576
1.889034 5.190400
-0.798747 2.185588
2.836520 -2.658556
-3.837877 -3.253815
2.096701 3.886007
-2.709034 2.923887
3.367037 -3.184789
-2.121479 -4.232586
2.329546 3.179764
-3.284816 3.273099
3.091414 -3.815232
-3.762093 -2.432191
3.542056 2.778832
-1.736822 4.241041
2.127073 -2.983680
-4.323818 -3.938116
3.792121 5.135768
-4.786473 3.358547
2.624081 -3.260715
-4.009299 -2.978115
2.493525 1.963710
-2.513661 2.642162
1.864375 -3.176309
-3.171184 -3.572452
2.894220 2.489128
-2.562539 2.884438
3.491078 -3.947487
-2.565729 -2.012114
3.332948 3.983102
-1.616805 3.573188
2.280615 -2.559444
-2.651229 -3.103198
2.321395 3.154987
-1.685703 2.939697
3.031012 -3.620252
-4.599622 -2.185829
4.196223 1.126677
-2.133863 3.093686
4.668892 -2.562705
-2.793241 -2.149706
2.884105 3.043438
-2.967647 2.848696
4.479332 -1.764772
-4.905566 -2.911070
结果为:
k=5时
k=6时
收录于合集 #算法
个
上一篇GPS抽稀之道格拉斯-普克(Douglas-Peuker)算法下一篇Matlab RBF神经网络及其实例
标签:Means,centroids,dataSet,cluster,np,算法,数据挖掘,质心 From: https://blog.51cto.com/domi/5789461