09 机器学习 - Kmeans聚类算法案例

1. 需求

对给定的数据集进行聚类

本案例采用二维数据集，共80个样本，有4个类。样例如下（testSet.txt）：

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

2. python代码实现

2.1 利用numpy手动实现

from numpy import *
#加载数据
def loadDataSet(fileName):
    dataMat = []
    fr = open(fileName)
    for line in fr.readlines():
        curLine = line.strip().split('\t')
        fltLine = map(float, curLine)    #变成float类型
        dataMat.append(fltLine)
    return dataMat

# 计算欧几里得距离
def distEclud(vecA, vecB):
    return sqrt(sum(power(vecA - vecB, 2)))

#构建聚簇中心，取k个(此例中为4)随机质心
def randCent(dataSet, k):
    n = shape(dataSet)[1]
    centroids = mat(zeros((k,n)))   #每个质心有n个坐标值，总共要k个质心
    for j in range(n):
        minJ = min(dataSet[:,j])
        maxJ = max(dataSet[:,j])
        rangeJ = float(maxJ - minJ)
        centroids[:,j] = minJ + rangeJ * random.rand(k, 1)
    return centroids

#k-means 聚类算法
def kMeans(dataSet, k, distMeans =distEclud, createCent = randCent):
    m = shape(dataSet)[0]
    clusterAssment = mat(zeros((m,2)))    #用于存放该样本属于哪类及质心距离
    centroids = createCent(dataSet, k)
    clusterChanged = True
    while clusterChanged:
        clusterChanged = False;
        for i in range(m):
            minDist = inf; minIndex = -1;
            for j in range(k):
                distJI = distMeans(centroids[j,:], dataSet[i,:])
                if distJI < minDist:
                    minDist = distJI; minIndex = j
            if clusterAssment[i,0] != minIndex: clusterChanged = True;
            clusterAssment[i,:] = minIndex,minDist**2
        print centroids
        for cent in range(k):
            ptsInClust = dataSet[nonzero(clusterAssment[:,0].A == cent)[0]]   # 去第一列等于cent的所有列
            centroids[cent,:] = mean(ptsInClust, axis = 0)
    return centroids, clusterAssment

2.2 利用scikili库实现

Scikit-Learn是基于python的机器学习模块，基于BSD开源许可证。

scikit-learn的基本功能主要被分为六个部分，分类，回归，聚类，数据降维，模型选择，数据预处理。包括SVM，决策树，GBDT，KNN，KMEANS等等。

Kmeans在scikit包中即已有实现，只要将数据按照算法要求处理好，传入相应参数，即可直接调用其kmeans函数进行聚类。

#################################################
# kmeans: k-means cluster
#################################################
from numpy import *
import time
import matplotlib.pyplot as plt
## step 1:加载数据
print "step 1: load data..."
dataSet = []
fileIn = open('E:/Python/ml-data/kmeans/testSet.txt')
for line in fileIn.readlines():
	lineArr = line.strip().split('\t')
	dataSet.append([float(lineArr[0]), float(lineArr[1])])
## step 2: 聚类
print "step 2: clustering..."
dataSet = mat(dataSet)
k = 4
centroids, clusterAssment = kmeans(dataSet, k)
## step 3:显示结果
print "step 3: show the result..."
showCluster(dataSet, k, centroids, clusterAssment)

2.3 运行结果

不同的类用不同的颜色来表示，其中的大菱形是对应类的均值质心点。