Kmeans算法

原创于 2021-03-20 18:06:06 发布 · 254 阅读

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文章标签：

#Kmeans #biKmeans #数据挖掘

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C++实现：

#include <bits/stdc++.h>
using namespace std;
const int MAX = 1e6+10;
struct hh{
	double x,y;
}a[MAX],b[MAX],c[MAX];
int k,n;
vector<int> vv[MAX];
void init(){
	ifstream in("texts.txt");
	string s;
	int cnt=0;
	while(getline(in,s)){//着行读取数据并存于s中，直至数据全部读取
		cnt++;
		int sum=0;
		int index;
		for (int i = 0; i < s.size();i++){
			if(s[i]!='	'){
				sum=sum*10+(s[i]-'0');
			}
			else{
				a[cnt].x=sum;
				index=i+1;
				break;
			}
		}
		sum=0;
		for (int i = index; i < s.size();i++){
			sum=sum*10+(s[i]-'0');
		}
		a[cnt].y=sum;
	}
	n=cnt;
}
bool f=false;
bool judge(){
	bool ff=true;
	for (int i = 1; i <= k;i++){
		double xx=0;
		double yy=0;
		for (int j = 0; j < vv[i].size();j++){
			xx+=a[vv[i][j]].x;
			yy+=a[vv[i][j]].y;
		}
		if(vv[i].size()!=0){
			xx/=vv[i].size();
			yy/=vv[i].size();
			c[i].x=xx;
			c[i].y=yy;
		}
		if(xx!=b[i].x||yy!=b[i].y){
			ff=false;
		}
	}
	if(ff) return true;
	else return false;
}
void kms(int x){
	if(f) return;
	if(x==0){
		for (int i = k+1; i <= n;i++){
			b[i-k].x=a[i-k].x;
			b[i-k].y=a[i-k].y;
			vv[i-k].push_back(i-k);
			double minn=1e9;
			int index=0;
			for (int j = 1; j <= k;j++){
				double ww=(a[i].x-a[j].x)*(a[i].x-a[j].x)+(a[i].y-a[j].y)*(a[i].y-a[j].y);
				if(ww<minn){
					minn=ww;
					index=j;
				}
			}
			vv[index].push_back(i);
		}
		f=judge();
		if(f) return;
		else{
			for (int i = 1; i <= k;i++){
				vv[i].clear();
				b[i].x=c[i].x;
				b[i].y=c[i].y;
			}
			kms(x+1);
		}
	}
	else{
		for (int i = 1; i <= n;i++){
			double minn=1e9;
			int index=0;
			for (int j = 1; j <= k;j++){
				double ww=(a[i].x-b[j].x)*(a[i].x-b[j].x)+(a[i].y-b[j].y)*(a[i].y-b[j].y);
				if(ww<minn){
					minn=ww;
					index=j;
				}
			}
			vv[index].push_back(i);
		}
		f=judge();
		if(f) return;
		else{
			for (int i = 1; i <= k;i++){
				vv[i].clear();
				b[i].x=c[i].x;
				b[i].y=c[i].y;
			}
			kms(x+1);
		}
	}
}
int main(){
	init();
	printf("请输入k:");
	scanf("%d",&k);
	kms(0);
	for (int i = 1; i <= k;i++){
		printf("%f %f\n",c[i].x,c[i].y);
		for (int j = 0; j < vv[i].size();j++){
			printf("%d ",vv[i][j]);
		}
		puts("");
	} 
	return 0;
}

Python实现：

# encoding: utf-8
#导入tests.txt中的数据，利用K均值算法对进行分类
from numpy import *
import matplotlib.pyplot as plt

def loadDataSet(fileName): #读入数据
    dataSet = []
    f = open(fileName)
    for line in f.readlines():
        curLine = line.strip().split('\t') #读入一行 形式为字符串
        fltLine = list(map(float, curLine)) #转换成浮点型
        dataSet.append(fltLine)
    return mat(dataSet) #转换成矩阵

#求两个向量的欧式距离
def distEclud(vecA, vecB):
    return sum(power(vecA - vecB, 2))

def randCent(dataSet, k):
    n = shape(dataSet)[1] #n是列数
    center = mat(zeros((k, n))) #初始化矩阵
    for j in range(n):
        minJ = min(dataSet[:, j]) #找到第j列最小值
        rangeJ = float(max(dataSet[:, j]) - minJ) #求第j列最大值与最小值的差
        center[:, j] = minJ + rangeJ * random.rand(k, 1) #生成k行1列的在(0, 1)之间的随机数矩阵
    return center

def KMeans(dataSet, k, distMeas=distEclud, createCent=randCent):
    m = shape(dataSet)[0] #数据集的行
    initM = mat(zeros((m, 2))) #初始化矩阵
    center = createCent(dataSet, k)
    flag = True
    while flag:
        flag = False
        for i in range(m): #遍历数据集中的每一行数据
            minDist = inf; minIndex = -1
            for j in range(k): #寻找最近质心
                distJI = distMeas(center[j, :], dataSet[i, :])
                if distJI < minDist: #更新最小距离和质心下标
                    minDist = distJI; minIndex = j
            if initM[i, 0] != minIndex:
                flag = True
            initM[i, :] = minIndex, minDist #记录最小距离质心下标，最小距离的平方
        for cent in range(k): #更新质心位置
            ptsInClust = dataSet[nonzero(initM[:,0].A==cent)[0]] #获得距离同一个质心最近的所有点的下标，即同一簇的坐标
            center[cent,:] = mean(ptsInClust, axis=0) #求同一簇的坐标平均值，axis=0表示按列求均值
    return center, initM

def showCluster(dataSet, k, initM, center): #画图表示,从网上学的
    fig = plt.figure()
    ax = fig.add_subplot(111)
    plt.title("K-means")
    data = []
    for cent in range(k): #提取出每个簇的数据
        ptsInClust = dataSet[nonzero(initM[:,0].A==cent)[0]] #获得属于cent簇的数据
        data.append(ptsInClust)
    for cent, c, marker in zip( range(k), ['r', 'g', 'b', 'y'], ['^', 'o', '*', 's'] ): #画出数据点散点图
        ax.scatter(array(data[cent][:, 0]), array(data[cent][:, 1]), s=80, c=c, marker=marker)
    ax.scatter(array(center[:, 0]), array(center[:, 1]), s=1000, c='black', marker='+', alpha=1) #画出质心点
    ax.set_xlabel('X Label')
    ax.set_ylabel('Y Label')
    plt.show()

if __name__ == "__main__":
    dataSet = loadDataSet('texts.txt')
    print("请输入k：")
    k=int(input())
    center, initM = KMeans(dataSet, k)
    showCluster(dataSet, k, initM,center) #画图表示,从网上学的

数据：texts.txt

1   1
2   1
1   2
2   2
4   3
5   3
4   4
5   4

优化biKmeans

# encoding: utf-8
#导入tests.txt中的数据，利用K均值算法对进行分类
from numpy import *
import matplotlib.pyplot as plt

def loadDataSet(fileName): #读入数据
    dataSet = []
    f = open(fileName)
    for line in f.readlines():
        curLine = line.strip().split('\t') #读入一行 形式为字符串
        fltLine = list(map(float, curLine)) #转换成浮点型
        dataSet.append(fltLine)
    return mat(dataSet) #转换成矩阵

#求两个向量的欧式距离
def distEclud(vecA, vecB):
    return sum(power(vecA - vecB, 2))

def randCent(dataSet, k):
    n = shape(dataSet)[1] #n是列数
    center = mat(zeros((k, n))) #初始化矩阵
    for j in range(n):
        minJ = min(dataSet[:, j]) #找到第j列最小值
        rangeJ = float(max(dataSet[:, j]) - minJ) #求第j列最大值与最小值的差
        center[:, j] = minJ + rangeJ * random.rand(k, 1) #生成k行1列的在(0, 1)之间的随机数矩阵
    return center

def KMeans(dataSet, k, distMeas=distEclud, createCent=randCent):
    m = shape(dataSet)[0] #数据集的行
    initM = mat(zeros((m, 2))) #初始化矩阵
    center = createCent(dataSet, k)
    flag = True
    while flag:
        flag = False
        for i in range(m): #遍历数据集中的每一行数据
            minDist = inf; minIndex = -1
            for j in range(k): #寻找最近质心
                distJI = distMeas(center[j, :], dataSet[i, :])
                if distJI < minDist: #更新最小距离和质心下标
                    minDist = distJI; minIndex = j
            if initM[i, 0] != minIndex:
                flag = True
            initM[i, :] = minIndex, minDist #记录最小距离质心下标，最小距离的平方
        for cent in range(k): #更新质心位置
            ptsInClust = dataSet[nonzero(initM[:,0].A==cent)[0]] #获得距离同一个质心最近的所有点的下标，即同一簇的坐标
            center[cent,:] = mean(ptsInClust, axis=0) #求同一簇的坐标平均值，axis=0表示按列求均值
    return center, initM

def biKmeans(dataSet, k, distMeas=distEclud):
    m = shape(dataSet)[0] #数据集的行
    initM = mat(zeros((m,2))) #初始化矩阵
    centroid0 = mean(dataSet, axis=0) #求所有数据的平均值，axis=0表示按列求均值
    centList =[centroid0]
    for j in range(m): #计算初始误差平方和
        initM[j,1] = distMeas(mat(centroid0), dataSet[j,:])
    while (len(centList) < k): #只要聚类的个数小于等于k
        lowestSSE = inf
        for i in range(len(centList)):
            ptsInCurrCluster = dataSet[nonzero(initM[:,0].A==i)[0],:] #获得属于cent簇的数据
            centroidMat, splitClustAss = KMeans(ptsInCurrCluster, 2, distMeas) #对一个簇中的数据进行kMeans
            sseSplit = sum(splitClustAss[:,1]) #计算本次划分误差平方和
            sseNotSplit = sum(initM[nonzero(initM[:,0].A!=i)[0],1]) #计算不属于cent簇的误差平方和
            print ("sseSplit, and notSplit: ",sseSplit,sseNotSplit)
            if (sseSplit + sseNotSplit) < lowestSSE: #如果有效降低了误差平方和，则记录
                bestCentToSplit = i
                bestNewCents = centroidMat
                bestClustAss = splitClustAss.copy()
                lowestSSE = sseSplit + sseNotSplit
        bestClustAss[nonzero(bestClustAss[:,0].A == 1)[0],0] = len(centList) #将划分簇的编号转为新加簇的编号
        bestClustAss[nonzero(bestClustAss[:,0].A == 0)[0],0] = bestCentToSplit #更新原始的该簇质心编号
        print ('the bestCentToSplit is: ',bestCentToSplit)
        print ('the len of bestClustAss is: ', len(bestClustAss))
        centList[bestCentToSplit] = bestNewCents[0,:].tolist()[0]#将一个质心更新为两个质心
        centList.append(bestNewCents[1,:].tolist()[0])
        initM[nonzero(initM[:,0].A == bestCentToSplit)[0],:]= bestClustAss #更新数据的编号以及误差平方和
    return mat(centList), initM

def showCluster(dataSet, k, initM, center): #画图表示,从网上学的
    fig = plt.figure()
    ax = fig.add_subplot(111)
    plt.title("K-means")
    data = []
    for cent in range(k): #提取出每个簇的数据
        ptsInClust = dataSet[nonzero(initM[:,0].A==cent)[0]] #获得属于cent簇的数据
        data.append(ptsInClust)
    for cent, c, marker in zip( range(k), ['r', 'g', 'b', 'y'], ['^', 'o', '*', 's'] ): #画出数据点散点图
        ax.scatter(array(data[cent][:, 0]), array(data[cent][:, 1]), s=80, c=c, marker=marker)
    ax.scatter(array(center[:, 0]), array(center[:, 1]), s=1000, c='black', marker='+', alpha=1) #画出质心点
    ax.set_xlabel('X Label')
    ax.set_ylabel('Y Label')
    plt.show()

if __name__ == "__main__":
    dataSet = loadDataSet('texts.txt')
    print("请输入k：")
    k=int(input())
    #center, initM = KMeans(dataSet, k)
    center, initM = biKmeans(dataSet, k) #从网上学的
    print(center) #中心点
    print(initM) #第一维表示距离哪个中心点最近，第二维表示距离最近中心点的距离
    showCluster(dataSet, k, initM,center) #画图表示,从网上学的

数据：texts.txt

1   1
2   1
1   2
2   2
4   3
5   3
4   4
5   4